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  • 1
    Electronic Resource
    Electronic Resource
    A finite element convergence analysis for 3D Stokes equations in case of variational crimes (2000)
    Springer
    Applications of mathematics 45 (2000), S. 99-129 
    Details
    ISSN: 1572-9109
    Keywords: Stokes equations ; nonstandard boundary conditions ; finite element method ; approximation of boundary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022235512626
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  • 2
    Electronic Resource
    Electronic Resource
    Evanescent energy in square and circular fibers (2000)
    Springer
    Journal of mathematical chemistry 27 (2000), S. 251-265 
    Details
    ISSN: 1572-8897
    Keywords: evanescent energy ; optical fibers ; single-molecule detection ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A finite element method is presented to find the propagation characteristics of an optical fiber with arbitrary cross section. This method uses a non-local boundary operator to reduce the infinite problem (open waveguide) to a bounded one. Evanescent energy in circular and square fibers of the same core area are computed and compared to show that square fibers can be effectively used in single molecule detection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018889304472
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  • 3
    Electronic Resource
    Electronic Resource
    Parallel linear multigrid by agglomeration for the acceleration of 3D compressible flow calculations on unstructured meshes (2000)
    Springer
    Numerical algorithms 24 (2000), S. 309-332 
    Details
    ISSN: 1572-9265
    Keywords: computational fluid dynamics ; Navier–Stokes equations ; finite element method ; finite volume method ; multigrid algorithm ; parallel computing ; 76N10 ; 76M10 ; 65M55 ; 65Y05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we report on our recent efforts concerning the design of parallel linear multigrid algorithms for the acceleration of 3-dimensional compressible flow calculations. The multigrid strategy adopted in this study relies on a volume agglomeration principle for the construction of the coarse grids starting from a fine discretization of the computational domain. In the past, this strategy has mainly been studied in the 2-dimensional case for the solution of the Euler equations (see Lallemand et al. [6]), the laminar Navier–Stokes equations (see Mavriplis and Venkatakrishnan [12]) and the turbulent Navier–Stokes equations (see Carré [1], Mavriplis [10] and Francescatto and Dervieux [4]). A first extension to the 3-dimensional case is presented by Mavriplis and Venkatakrishnan in [13] and more recently in Mavriplis and Pirzadeh [11]. The main contribution of the present work is twofold: on the one hand, we demonstrate the successful extension and application of the multigrid by a volume agglomeration principle to the acceleration of complex 3-dimensional flow calculations on unstructured tetrahedral meshes and, on the other hand, we enhance further the efficiency of the methodology through its adaptation to parallel architectures. Moreover, a nontrivial aspect of this work is that the corresponding software developments are taking place in an existing industrial flow solver.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019161730732
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical Methods for Accurate Computation of Design Sensitivities for Two-Dimensional Navier-Stokes Problems (2000)
    Springer
    Optimization and engineering 1 (2000), S. 277-304 
    Details
    ISSN: 1573-2924
    Keywords: fluid flow ; finite element method ; Navier-Stokes ; partial differential equations ; projections ; design sensitivity analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Gradient computations can be a limiting factor in algorithm efficiency and accuracy for optimization based design. In this paper, we present three parameterized flow problems and consider the evaluation of state sensitivities both theoretically and numerically. Existence and uniqueness results are given for the sensitivities of a specific group of two-dimensional Navier-Stokes problems. We then turn our attention to obtaining numerical approximations to state sensitivities. We show convergence of our numerical sensitivities using a problem having an exact solution. Next, two problems, flow around a cylinder and flow over a bump, are used to evaluate several computational schemes. In particular, a local projection scheme for improved state derivative approximations and the use of an adaptive finite element scheme are shown to be important techniques for obtaining accurate sensitivity approximations. Lastly, we evaluate the impact of these computational techniques on cost function and gradient calculation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010026123124
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  • 5
    Electronic Resource
    Electronic Resource
    Comprehensive mathematical model of microcirculatory dynamics (II)—Calculation and the results (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 579-584 
    Details
    ISSN: 1573-2754
    Keywords: influence line method ; analytical method ; finite element method ; microcirculatory dynamics ; O368 ; O242.1
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The mathematical model described in Part I was solved using “influence line method” combining analytical method and finite element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefore not important that interstitial fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation can meet metabolic need some extent in the form of dynamic equilibrium. The property of arteriole as a “resistant vessel” and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical model developed in Part I is physiologically resonable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459040
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  • 6
    Electronic Resource
    Electronic Resource
    A new method for stress analysis of a cyclically symmetric structure (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 87-94 
    Details
    ISSN: 1573-2754
    Keywords: cyclically symmetric structure ; finite element method ; stress analysis ; O175.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, a computational method for finite element stress analysis of a cyclically symmetric structure subjected to arbitrary loads is provided. At first, using discrete Fourier transformation technique, the complete structure is analyzed by considering only one sector with appropriate complex constraints on its boundary with the adjacent sectors. Next, an imaginary structure which is composed of two identically overlapping sectors is constructed, and that the complex constraints mentioned above can be equivalently replaced by a set of real constraints on this imaginary struture is proved. Therefore, the stress analysis of a cyclically symmetric structure can be solved conveniently by most of finite element programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458544
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  • 7
    Electronic Resource
    Electronic Resource
    Penalty finite element method for nonlinear dynamic response of viscous fluid-saturated biphase porous media (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1381-1389 
    Details
    ISSN: 1573-2754
    Keywords: porous media ; viscous fluid ; dynamic response ; finite element method ; O347
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The governing equations as well as boundary and initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients on deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459216
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  • 8
    Electronic Resource
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    F E M analysis of delamination buckling in composite plates and shells (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 341-346 
    Details
    ISSN: 1573-2754
    Keywords: buckling ; composites ; delamination ; finite element method ; shells ; TB332 ; O242.21 ; O346.5 ; TG335.81
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The purpose of the present study is to develop a new finite element method for analyzing buckling of delaminated composite plates and shells. This is achieved by establishing a new finite element called the reference-surface element. By use of the compatibility condition under Mindlin assumptions, the formulation of the reference-surface element was derived from whichever plate-element or shell-element being capable of analyzing composite plates and shells. This method assures a reasonable description of displacement field and the satisfaction of compatibility conditions for delamination problem. Numerical results for linear delamination buckling of axially compressed shells are presented to validate the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459013
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  • 9
    Electronic Resource
    Electronic Resource
    The finite element method based on interpolating with wavelet basis function (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 13-18 
    Details
    ISSN: 1573-2754
    Keywords: wavelet analysis ; finite element method ; nonconforming analysis ; CLC number ; O242.21
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional, interpolating method is modified. The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pattern is eliminated by static condensation method. Finally, the wavelet finite element formulations based on variational principles are put forward.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458534
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  • 10
    Electronic Resource
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    Stabilization of algebraic multilevel iteration methods; additive methods (1999)
    Springer
    Numerical algorithms 21 (1999), S. 23-47 
    Details
    ISSN: 1572-9265
    Keywords: multilevel method ; stabilization ; finite element method ; additive method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract There exist two main versions of preconditioners of algebraic multilevel type, the additive and the multiplicative methods. They correspond to preconditioners in block diagonal and block matrix factorized form, respectively. Both can be defined and analysed as recursive two-by-two block methods. Although the analytical framework for such methods is simple, for many finite element approximations it still permits the derivation of the strongest results, such as optimal, or nearly optimal, rate of convergence and optimal, or nearly optimal order of computational complexity, when proper recursive global orderings of node points have been used or when they are applied for hierarchical basis function finite element methods for elliptic self-adjoint equations and stabilized in a certain way. This holds for general elliptic problems of second order, independent of the regularity of the problem, including independence of discontinuities of coefficients between elements and of anisotropy. Important ingredients in the methods are a proper balance of the size of the coarse mesh to the finest mesh and a proper solver on the coarse mesh. This paper presents in a survey form the basic results of such methods and considers in particular additive methods. This method has excellent parallelization properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019136808500
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  • 11
    Electronic Resource
    Electronic Resource
    Finite element analysis of wave propagation in fluid-saturated porous media (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 1331-1341 
    Details
    ISSN: 1573-2754
    Keywords: porous media ; wave propagation ; finite element method ; O347
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract With the porous media model based on mixture theory, a finite element formulation for dynamic transient analysis of fluid-saturated two-phase porous media is presented. Time integration of the equation, deduced with penalty method, can be performed by using implicit or explicit method. One-dimensional wave propagation in column under step loading and impulsive loading are analyzed with the developed finite element program. The obtained curves of displacements, velocities, effective stresses and pore pressures against time demonstrate the existence of wave propagation phenomena, which coincide with the theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459166
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  • 12
    Electronic Resource
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    Parameter-Free Elastic Deformation Approach for 2D and 3D Registration Using Prescribed Displacements (1999)
    Springer
    Journal of mathematical imaging and vision 10 (1999), S. 143-162 
    Details
    ISSN: 1573-7683
    Keywords: non-rigid medical image registration ; elasticity theory ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A parameter-free approach for non-rigid image registration based on elasticity theory is presented. In contrast to traditional physically-based numerical registration methods, no forces have to be computed from image data to drive the elastic deformation. Instead, displacements obtained with the help of mapping boundary structures in the source and target image are incorporated as hard constraints into elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model such as elastic constants. The approach guarantees the exact correspondence of boundary structures in the images assuming that correct input data are available. The implemented incremental method allows to cope with large deformations. The theoretical background, the finite element discretization of the elastic model, and experimental results for 2D and 3D synthetic as well as real medical images are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008375006703
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  • 13
    Electronic Resource
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    A spectral streamline diffusion finite element coupling method of unsteady transport equation in the field of neutron logging (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 739-747 
    Details
    ISSN: 1573-2754
    Keywords: neutron logging ; transport equation ; finite element method ; streamline diffusion ; O241.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element for unsteady Boltzmann equation in the neutron logging field, is discussed. The convergence and error estimations of this scheme are proved. Its applications in the field of neutron logging show its effectiveness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02454895
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  • 14
    Electronic Resource
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    A review of two different approaches for superconvergence analysis (1998)
    Springer
    Applications of mathematics 43 (1998), S. 401-411 
    Details
    ISSN: 1572-9109
    Keywords: finite element method ; superconvergence error estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023220520477
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  • 15
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    Finite element analysis of temperature field with phase transformation and non-linear surface heat-transfer coefficient during quenching (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 15-20 
    Details
    ISSN: 1573-2754
    Keywords: finite element method ; quenching ; heat conduction ; phase transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The calculation of temperature field has a great influence upon the analysis of the thermal stresses and strains during quenching, and also upon the residual stresses and microstructure of the workpiece after quenching, too. In this paper, a 42CrMo steel cylinder was taken as an investigating example. From the TTT diagram of the 42 CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as the functions of temperature and the volume fraction of phase constitutents. Finally, the temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated with finite element method, and the corresponding functional of temperature was established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458976
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  • 16
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    Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
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    ISSN: 0170-4214
    Keywords: generalized Stokes equations ; incompressible flow ; least-squares ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 17
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    Research on solid-liquid coupling dynamics of pipe conveying fluid (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 1065-1071 
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    ISSN: 1573-2754
    Keywords: finite element method ; pipe conveying fluid ; solid-fluid coupling vibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract On the basis of Hamilton principle, the equation of solid-liquid coupling vibration of pipe conveying fluid is deduced. An asymmetrical solid-liquid coupling damp matrix and a symmetrical solid-liquid coupling stiffness matrix are obtained. UsingQR method, pipe's nature frequencies are calculated. The curves of the first four orders of natural frequency-flow velocity of pipe waw given. The influence of flowing velocity, pressure, solid-liquid coupling damp and solid-liquid coupling stiffness on natural frequency are discussed respectively. The dynamic respondence of the pipes for stepload with different flow velocity are calculated by Newmark method. It is found that, with the flow velocity increased, the nature frequency of the pipes reduced, increased, reduced again and so on.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459195
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  • 18
    Electronic Resource
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    Simulation of surface tension effect during filling of a thin section cavity via an interface element (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
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    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
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  • 19
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    A finite element analysis of multiphase immiscible flow in deforming porous media for subsurface systems (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 135-149 
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    ISSN: 1069-8299
    Keywords: multiphase immiscible flow ; deforming porous media ; fully coupled ; soil displacements ; fluid pressures ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully coupled numerical model has been developed which describes multiphase fluid flow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase flow model, based on the two-phase flow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin finite element model which is subsequently used to simulate multiphase immiscible fluid flow under saturated and unsaturated conditions in porous media. The governing partial differential equations, in terms of soil displacements and fluid pressures, which are coupled and non-linear, are solved by the finite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. © 1998 John Wiley & Sons, Ltd.
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  • 20
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    Numerical visualization of oscillatory flow around a circular cylinder at Re=200 and KC=20 - an aperiodic flow case (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 181-194 
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    ISSN: 1069-8299
    Keywords: oscillating flow ; Keulegan-Carpenter number ; finite element method ; in-line force ; transverse force ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a numerical study of the viscous oscillating flow around a circular cylinder at Reynolds number=200 and Keulegan-Carpenter number=20 are presented. The finite element method was used for the solution of the Navier-Stokes equations, in the formulation where the streamfunction and the vorticity are the field variables. The computation revealed a complicated flow pattern at which the flow is not periodic but switches between different modes at various oscillation cycles. The vortex shedding patterns occurring at different cycles were identified by means of numerical flow visualization. The traces of the hydrodynamic forces were derived from the solution, and the hydrodynamic coefficients of the in-line force were evaluated. © 1998 John Wiley & Sons, Ltd.
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  • 21
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    Optimal control of vorticity in Rayleigh-Bernard convection by finite element method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 9-22 
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    ISSN: 1069-8299
    Keywords: finite element method ; optimal control theory ; Navier-Stokes equations ; Lagrange multipliers ; adjacent equations ; Sakawa-Shindo method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work presents control of vorticity for buoyancy-driven flows. The governing set of equations includes Navier-Stokes and heat transfer equations. The basic formulation for the control problem is derived using Lagrange multipliers and the Pontryagin minimum principle. Control values are found using the Sakawa-Shindo method. Control was accomplished using velocity components. Numerical examples present control of vorticity for Rayleigh-Bernard convection in an enclosed cavity for a wide range of Ra numbers. The current formulation proved reliable and fast. Optimal control was obtained and turned out to be adequate. © 1998 John Wiley & Sons, Ltd.
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  • 22
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    Computing ship wave resistance from wave amplitude with a non-local absorbing boundary condition (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 997-1012 
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    ISSN: 1069-8299
    Keywords: potential flow ; finite element method ; wave resistance ; absorbing boundary condition ; free surface flow ; partial discretization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non-negative wave-resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson-like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 23
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    Finite element computations for the Reissner-Mindlin plate model (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1119-1131 
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    ISSN: 1069-8299
    Keywords: Reissner-Mindlin plate ; finite element method ; p version ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the finite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be predicted numerically with great confidence near the boundary. We illustrate this through numerical computations in the case when both boundary layers and corner singularities are present. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 24
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    A pollution controlled hybrid interior error estimator for linear elastostatics (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 507-532 
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    ISSN: 0029-5981
    Keywords: adaptivity ; finite element method ; interior error estimates ; a posteriori error estimators ; hybrid interior error estimators ; pollution errors ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hybrid error estimator using a priori interior region estimates in an a posteriori framework is presented for linear elastostatics problems in FEA. It is shown that local rates of convergence are augmented by this technique and global rates are not adversely affected. The effects of pollution for this estimator are explained and a pollution error estimator is derived using the concept of error loads. It is shown that pollution error estimation can improve the performance of both the conventional a posteriori and the hybrid techniques. A series of numerical results are presented which demonstrate the superior performance of the proposed method over previously published interior error estimation techniques. © 1998 John Wiley & Sons, Ltd.
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    Modelling of muscle behaviour by the finite element method using Hill's three-element model (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 941-953 
    Details
    ISSN: 0029-5981
    Keywords: muscle model ; numerical stress calculation ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a numerical algorithm for the determination of muscle response by the finite element method. Hill's three-element model is used as a basis for our analysis. The model consists of one linear elastic element, coupled in parallel with one non-linear elastic element, and one non-linear contractile element connected in series. An activation function is defined for the model in order to describe a time-dependent character of the contractile element with respect to stimulation.Complex mechanical response of muscle, accounting for non-linear force-displacement relation and change of geometrical shape, is possible by the finite element method. In an incremental-iterative scheme of calculation of equilibrium configurations of a muscle, the key step is determination of stresses corresponding to a strain increment. We present here the stress calculation for Hill's model which is reduced to the solution of one non-linear equation with respect to the stretch increment of the serial elastic element. The muscle fibers can be arbitrarily oriented in space and we give a corresponding computational procedure of calculation of nodal forces and stiffness of finite elements.The proposed computational scheme is built in our FE package PAK, so that real muscles of complex three-dimensional shapes can be modelled. In numerical examples we illustrate the main characteristic of the developed numerical model and the possibilities of solution of real problems in muscle functioning. © 1998 John Wiley & Sons, Ltd.
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    Simulating three-dimensional stress intensity factors by the least-squares method (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1437-1451 
    Details
    ISSN: 0029-5981
    Keywords: crack ; finite element method ; J-integral ; least-squares method ; stress intensity factor ; three-dimensional ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The main purpose of this paper is to investigate the accuracy of the least-squares method incorporating the finite element method for finding three-dimensional (3-D) Stress Intensity Factors (SIFs). Numerical simulations in this paper indicate that the least-squares method can be used to calculate 3-D SIFs accurately, if three or more than three displacement or stress terms are included. The calculated SIFs of this method are independent of the maximum radius of the area from which data is included; furthermore, a very fine mesh is not necessary. © 1998 John Wiley & Sons, Ltd.
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    A shear-flexible element with warping for thin-walled open beams (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1173-1191 
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    ISSN: 0029-5981
    Keywords: warping ; bimoment ; Vlasov's thin-walled beam ; block stiffness matrix ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element for the analysis of thin-walled open beams with an arbitrary cross section is presented. Combining Timoshenko beam theory and Vlasov thin-walled beam theory, the derived element includes both flexural shear deformations and warping deformations caused by the bimoment. By adopting an orthogonal Cartesian co-ordinate system, one can obviate the ad hoc introduction of St. Venant stiffness. The derived block stiffness matrix is comparable but more general than the one given by earlier researchers. The versatility and accuracy of the new element are demonstrated by comparing the numerical results with the classical solutions or other numerical results available in the literature. © 1998 John Wiley & Sons, Ltd.
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    Optimal process design in non-isothermal, non-steady metal forming by the finite element method (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 1343-1390 
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    ISSN: 0029-5981
    Keywords: optimal design ; design sensitivity ; direct differentiation method ; non-isothermal ; metal forming ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to process optimal design in non-isothermal, non-steady-state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo-mechanical finite element process model so as to cover diverse objective functions and design variables, and a derivative-based approach is adopted for conducting optimization. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach to deal with diverse process parameters and objective functions is demonstrated through applications to some selected process design problems. © 1998 John Wiley & Sons, Ltd.
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    Simulation of surface pitting due to contact loading (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 33-50 
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    ISSN: 0029-5981
    Keywords: contact problems ; material fatigue ; pitting ; fracture mechanics ; finite element method ; experiments ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational model for simulation of surface pitting of mechanical elements subjected to rolling and sliding contact conditions is presented. The two-dimensional computational model is restricted to modelling of high-precision mechanical components with fine surface finishing and good lubrication, where the cracks leading to pitting are initiated in the area of largest contact stresses at certain depth under the contacting surface. Hertz contact conditions with addition of friction forces are assumed and the position and magnitude of the maximum equivalent stress is determined by the finite element method. When the maximum equivalent stress exceeds the local material strength, it is assumed that the initial crack develops along the slip line in a single-crystal grain. The Virtual Crack Extension method in the framework of finite element analysis is then used for two-dimensional simulation of the fatigue crack propagation under contact loading from the initial crack up to the formation of the surface pit. The pit shapes and relationships between the stress intensity factor and crack length are determined for various combinations of contacting surface curvatures and loadings. The model is applied to simulation of surface pitting of two meshing gear teeth. Numerically predicted pit shapes in the face of gear teeth show a good agreement with the experimental observations. © 1998 John Wiley & Sons, Ltd.
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    Adaptive selection of polynomial degrees on a finite element mesh (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 561-578 
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    ISSN: 0029-5981
    Keywords: finite element method ; adaptivity ; a posteriori error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector field computed from the finite element solution. This estimator, designed for p- and hp-extensions, is conceptually different from estimators based on residuals or patch recovery which are designed for h-extension procedures. The quality of the error estimator is demonstrated by examples. The results show that the effectivity index is reasonably close to unity and the sequences of p-distributions obtained with the error indicators closely follow the optimal trajectory. © 1998 John Wiley & Sons, Ltd.
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    Error estimation based on Superconvergent Patch Recovery using statically admissible stress fields (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 443-472 
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    ISSN: 0029-5981
    Keywords: finite element method ; error estimation ; stress recovery ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress field. The qualitative properties of the recovered stress field necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A specific procedure for recovery of an improved stress field is then developed. The procedure can be classified as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisfied a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. © 1998 John Wiley & Sons, Ltd.
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    Direct determination of asymptotic structural postbuckling behaviour by the finite element method (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 685-702 
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    ISSN: 0029-5981
    Keywords: asymptotic postbuckling ; stability ; finite element method ; smooth stresses ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution, the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick convergence of the postbuckling coefficients. © 1998 John Wiley & Sons, Ltd.
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    Automatic 3-D mode I crack propagation calculations with finite elements (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 739-757 
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    ISSN: 0029-5981
    Keywords: finite element method ; crack propagation ; low cycle fatigue ; remeshing ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented which allows for fully automatic linear elastic low cycle fatigue (LCF) crack propagation calculations of mode I plane cracks in large structures by means of the finite element technique. The bulk of the algorithm consists of an automatic procedure to introduce the geometry of a plane crack with an arbitrary crack front in an existing three-dimensional (3-D) mesh. Once the K-distribution for the initial crack has been calculated, the use of the superelement technique reduces the computing time for the subsequent cycles by a factor of up to 40 or more. Two industrial examples illustrate the accuracy and effectiveness of the method. © 1998 John Wiley & Sons, Ltd.
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    A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 219-236 
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    ISSN: 0029-5981
    Keywords: secant and tangent stiffness matrices ; structural analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non-linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application. © 1998 John Wiley & Sons, Ltd.
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    Iteratively-improved Robin boundary conditions for the finite element solution of scattering problems in unbounded domains (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 601-629 
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    ISSN: 0029-5981
    Keywords: finite element method ; scattering problems ; open boundaries ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative procedure is described for the finite-element solution of scalar scattering problems in unbounded domains. The scattering objects may have multiple connectivity, may be of different materials or with different boundary conditions. A fictitious boundary enclosing all the objects involved is introduced. An appropriate Robin (mixed) condition is initially guessed on this boundary and is iteratively improved making use of Green's formula. It will be seen that the best choice for the Robin boundary condition is an absorbing-like one. A theorem about the theoretical convergence of the procedure is demonstrated. An analytical study of the special case of a circular cylindrical scatterer is made. Comparisons are made with other methods. Some numerical examples are provided in order to illustrate and validate the procedure and to show its applicability whatever the frequency of the incident wave. Although particular emphasis is laid in the paper on electromagnetic problems, the procedure is fully applicable to other kinds of physical phenomena such as acoustic ones. © 1998 John Wiley & Sons, Ltd.
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    Cutting of a 3-D finite element mesh for automatic mode I crack propagation calculations (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 749-772 
    Details
    ISSN: 0029-5981
    Keywords: crack ; propagation ; remeshing ; mode-I ; three-dimensional ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A previous article (G. Dhondt, ‘Automatic 3-D mode I crack propagation calculations with finite elements’, Int. J. Numer. Meth. Engng. 41, 739-757 (1998)) has illustrated how automatic 3-D mode I cyclic crack propagation calculations making repeated use of the finite element method can be performed for structures in which the crack plane is made up of element faces. In the present paper an automatic cutting procedure is proposed which allows the method to be applied to arbitrarily meshed structures for which the crack plane intersects the elements. New 20-node brick elements are automatically generated and a subsequent smoothing procedure improves the quality of the resulting mesh. The method is illustrated by cyclic crack propagation calculations in a specimen and an industrial component. © 1998 John wiley & Sons, Ltd.
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    A new strategy for the solution of frictional contact problems (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1053-1068 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; variational inequalities ; contact problems ; heuristic algorithms ; nondifferential optimization methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article is devoted to the development of a new heuristic algorithm for the solution of the general variational inequality arising in frictional contact problems. The existing algorithms devised for the treatment of the variational inequality representing frictional contact rely on the decomposition of the physical problem into two sub-problems which are then solved iteratively. In addition, the penalty function method and/or the regularization techniques are typically used in the solution of these reduced sub-problems. These techniques introduce user-defined parameters which could influence the convergence and accuracy of the solution. The new method presented in this article overcomes these difficulties by providing a solution for the general variational inequality without decomposition into sub-problems. This is accomplished using a new heuristic algorithm which utilizes mathematical programming techniques, and thus avoids the use of penalty or regularization methods. The versatility and reliability of the developed algorithm were demonstrated through implementation to the case of frictional contact of an elastic hollow cylinder with a rigid foundation. © 1998 John Wiley & Sons, Ltd.
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    Finite element solution for the continuum traffic equilibrium problems (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1253-1273 
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    ISSN: 0029-5981
    Keywords: finite element method ; continuum modelling ; traffic equilibrium ; user-optimal pattern ; fixed demand ; variable demand ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we consider a city with a highly compact Central Business District (CBD), and the commuters’ destinations from the CBD are dispersed over the whole city. The street network is approximated as a continuum and commuters’ movements in the city are measured by the flow intensity, and the local travel cost depends on the location and the traffic flow intensity. We extend the continuum user equilibrium problem to deal with the case of variable demand, in which the traffic demand from any destination in the city to the CBD is assumed to be a function of both the destination location and the total travel cost to the CBD. An equivalent mathematical model is formulated and proved to satisfy the user equilibrium conditions, which is then solved by a finite element solution algorithm. Numerical examples are given to illustrate the effectiveness of the proposed method. © 1998 John Wiley & Sons, Ltd.
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    A first-second order splitting method for a third-order partial differential equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 89-96 
    Details
    ISSN: 0749-159X
    Keywords: finite element method ; third-order differential equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89-96, 1998
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    Convergence analysis of a finite volume method via a new nonconforming finite element method (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 213-231 
    Details
    ISSN: 0749-159X
    Keywords: cell-centered finite volume method ; convergence ; finite element method ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213-231, 1998
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    Least squares methods for Volterra equations and generalizations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 679-693 
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    ISSN: 0749-159X
    Keywords: least squares method ; finite element method ; Volterra equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679-693, 1998
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    On a certain two-sided symmetric condition in magnetic field analysis and computations (1997)
    Springer
    Applications of mathematics 42 (1997), S. 147-159 
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    ISSN: 1572-9109
    Keywords: magnetic field ; variational formulation ; two-sided existence and uniqueness condition ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.
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    Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method (1997)
    Springer
    Applications of mathematics 42 (1997), S. 259-277 
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    ISSN: 1572-9109
    Keywords: Parameter identification ; parabolic problem ; finite element method ; Crank-Nicolson scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
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    Numerical bifurcation and stability analysis for steady-states of reaction diffusion equations (1997)
    Springer
    Numerical algorithms 14 (1997), S. 211-225 
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    ISSN: 1572-9265
    Keywords: bifurcation function ; elliptic boundary value problem ; finite element method ; reduction to an alternative problem ; stability of steady-states ; 35J25 ; 65N35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Solutions $$u \in H_0^1 (\Omega ) \cap H^2 (\Omega )$$ of a semilinear elliptic boundary value problem, $$Au + f(x,u,\lambda ) = 0$$ (with $$f_u (x,u,\lambda )$$ bounded below) can be put into a one-to-one correspondence with zeros $$c \in \mathbb{R}^d $$ of a function $$c \to B(c,\lambda ) \in \mathbb{R}^d $$ . Often d is small. The function $$B(c,\lambda )$$ is called the bifurcation function. It can also be shown that the eigenvalues of the matrix $$B_c (c,\lambda )$$ characterize the stability properties of the solutions of the elliptic problem as rest points of $$u_t + Au + f(x,u,\lambda ) = 0$$ . A finite element method that can be used for computing B and B c has recently been proposed. An overview of these results and the finite element method is given.
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    The optimal control variational principle and finite elements analysis for viscoplastic dynamics (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 61-68 
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    ISSN: 1573-2754
    Keywords: viscoplastic dynamics ; optimal control ; variational principle ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.
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    A modified Hellinger-Reissner variational functional including only two independent variables for large displacement of thin shallow shell (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 663-670 
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    ISSN: 1573-2754
    Keywords: variational principle ; shallow shell ; large displacement ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with an arbitrary shape is first established. Then the functional of the modified principle suitable for the finite element method is derived. In the functional only two independent variables, the deflection ω and the stress function F are included. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.
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    Finite Element Approximation of Vector-Valued Hemivariational Problems (1997)
    Springer
    Journal of global optimization 10 (1997), S. 17-35 
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    ISSN: 1573-2916
    Keywords: vector-valued hemivariational inequality ; finite element method ; nonconvex energy function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we develop a finite element approximationfor vector-valuedhemivariational inequalities.This class of hemivariational problems wasintroducedin [12],[13]. We study two differentproblems: unconstrained oneand constrained one witha nonempty, closed, convex constraint set K. We shall show firstly that the discrete problemsare solvable by usingconsequences of Kakutanifixed point theorem and secondly that the solutionsof the discrete problemsare close on subsequences to the continuous ones.
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    Numerical methods for scattering problems by curved gratings at high frequencies (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
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    ISSN: 0170-4214
    Keywords: gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    IMPROVING MODULARITY IN OBJECT-ORIENTED FINITE ELEMENT PROGRAMMING (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; software engineering ; object-oriented programming ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Making a finite element code easier to maintain is achieved by further modularizing it. Due to its two levels of modularity (of procedures and data), object-oriented programming is the method of choice. Its potential is investigated in two bottlenecks of finite element programming where so far it has not proved significantly more successful than classical Fortran programming. The first of these is the lack of adequate data structures between the analysis specifications and the basic objects of the finite element method, like the element and the node. This is solved by defining two classes of objects, namely problem and domain, with clearly differentiated specifications. The second gap deals with solving linear equation systems. Introducing an intermediate class UnassembledMatrix allows alternative storage/solving schemes to be implemented in a very flexible manner. © 1997 by John Wiley & Sons, Ltd.
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    AN EXACT STRUCTURAL STATIC REANALYSIS METHOD (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 103-112 
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    ISSN: 1069-8299
    Keywords: static reanalysis ; finite element method ; structural analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd.
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    HOMOGENIZATION OF PERIODIC MASONRY: PLANE STRESS, GENERALIZED PLANE STRAIN OR 3D MODELLING? (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 319-326 
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    ISSN: 1069-8299
    Keywords: homogenization of periodic media ; masonry ; damage ; finite element method ; plane stress ; generalized plane strain ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Through the homogenization theory for periodic media, the macroscopic behaviour of masonry may be derived from the behaviour of its constitutive materials (brick and mortar). Such a procedure has been used by many authors but always in an approximate manner. In particular, masonry has been considered either as infinitely thin (two-dimensional media under plane stress), or as infinitely thick (two-dimensional media under generalized plane strain). In order to determine the range of validity of either assumption, the homogenization theory is here implemented in a rigorous way, i.e. taking into account the finite thickness of masonry. Both brick and mortar being assumed as subjected to isotropic damage, numerical computations show that the above-mentioned assumptions have little influence on the macroscopic elastic behaviour of masonry, but may significantly affect its non-linear response (ultimate load and mode of failure). © 1997 John Wiley & Sons, Ltd.
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    A COMPARISON BETWEEN SERENDIPITY AND LAGRANGE PLATE ELEMENTS IN THE FINITE ELEMENT METHOD (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 343-353 
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    ISSN: 1069-8299
    Keywords: plate element ; finite element method ; reduced integration ; penalty number ; Lagrange and serendipity elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The serendipity (eight nodes) and Lagrange (nine nodes) plate elements following the Reissner-Mindlin irreducible formulation for the bending of plates are among the most popular in the finite element method. However, reduced integration on the shearing part of the stiffness matrix has to be performed in order to avoid locking of the mesh in the limit of thin plates, where numerical constraints are taking some degrees of freedom in order to be satisfied. This paper explains the competition between those constraints and the degrees of freedom, giving a mean to predict whether a mesh will lock or not. It also shows why the Lagrange element performs better than the serendipity element. Numerical results confirm this analysis. © 1997 John Wiley & Sons, Ltd.
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    EVOLUTION OF POROSITY DISTRIBUTION FOR ONE-DIMENSIONAL PROBLEM OF VISCOUS SINTERING (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 355-372 
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    ISSN: 1069-8299
    Keywords: differential quadrature method ; finite element method ; porosity distribution ; powder metallurgy ; sintering ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Viscous sintering of a porous ball with various initial distributions of porosity versus radius is considered. For the solution of the corresponding boundary-value problems of the evolution of porosity and flow velocity fields during sintering, the numerical algorithms based on the differential quadrature method (DQM) and an arbitrary Eulerian-Lagrangian version of the finite element method (FEM) (the permeable element method) are elaborated. A comparative analysis of the calculation results is carried out. The question of the influence of non-uniformity of porosity distribution on the localization of densification is discussed. © 1997 John Wiley & Sons, Ltd.
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    Computational aspects of the natural-mode finite element method (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 705-713 
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    ISSN: 1069-8299
    Keywords: natural-modes ; finite element method ; model problem ; thermomechanical buckling ; computing statistics report ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We address here some computational aspects of the natural-mode finite element method (NM-FEM), a technique recently developed by the authors for the analysis of arbitrary composite shells. We consider in particular a model problem comprising a (45/-45/0/90)S cylindrical composite shell with 2398 degrees of freedom subjected to compressive load and temperature increase, and compute the first four critical loads and temperatures. For this problem a computational statistics report is obtained showing the breakdown of the CPU time in the various routines. It is observed that most of the computing time is spent on algebraic operations, suggesting computational efficiency and high potential for vectorization/parallelization. © 1997 John Wiley & Sons, Ltd.
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    Design sensitivity and constraint approximation methods for optimization in non-linear analysis (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
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    ISSN: 1069-8299
    Keywords: optimization ; sensitivity analysis ; constraint approximation ; non-linear analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the finite element non-linear analysis of engineering problems combined with an optimization method, two techniques - a semi-analytical sensitivity method and bi-point constraint approximation - have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more efficient than the finite difference method and the bi-point approximation gives results which compare favourably with the finite element results. © 1997 John Wiley & Sons, Ltd.
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    THE PARTITION OF UNITY METHOD (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 727-758 
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    ISSN: 0029-5981
    Keywords: finite element method ; meshless finite element method ; finite element methods for highly oscillatory solutions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a posteriori error estimation for this new method are also proved. © 1997 by John Wiley & Sons, Ltd.
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    AN EIGEN-FORCE METHOD FOR FINITE ELEMENT ANALYSIS AND REANALYSIS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 777-796 
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    ISSN: 0029-5981
    Keywords: finite element method ; force method ; reanalysis ; eigenvalue ; structural variation ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a force-based finite element method that involves eigen-space transformation of element stiffness matrices in the first analysis. In each subsequent analysis (‘reanalysis’) associated with structural variations, the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time-consuming task of solving a large system of equations. The structural variations may involve changes in material properties, birth or death of elements, or change in boundary conditions. Numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement-based finite element method. © 1997 by John Wiley & Sons, Ltd.
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    A MODEL STUDY OF THE QUALITY OF A POSTERIORI ERROR ESTIMATORS FOR FINITE ELEMENT SOLUTIONS OF LINEAR ELLIPTIC PROBLEMS, WITH PARTICULAR REFERENCE TO THE BEHAVIOR NEAR THE BOUNDARY (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2521-2577 
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    ISSN: 0029-5981
    Keywords: finite element method ; a posteriori error estimation ; asymptotic quality ; computer-based analysis ; effect of the boundary ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In References 1-3 we presented a computer-based theory for analysing the asymptotic accuracy (quality of robustness) of error estimators for mesh-patches in the interior of the domain. In this paper we review the approach employed in References 1-3 and extend it to analyse the asymptotic quality of error estimators for mesh-patches at or near a domain boundary. We analyse two error estimators which were found in References 1-3 to be robust in the interior of the mesh (the element residual with p-order equilibrated fluxes and (p+1)) degree bubble solution or (p+1) degree polynomial solution (ERpB or ERpPp+1; see References 1-3) and the Zienkiewicz-Zhu Superconvergent Patch Recovery (ZZ-SPR; see References 4-7) and we show that the robustness of these estimators for elements adjacent to the boundary can be significantly inferior to their robustness for interior elements. This deterioration is due to the difference in the definition of the estimators for the elements in the interior of the mesh and the elements adjacent to the boundary. In order to demonstrate how our approach can be employed to determine the most robust version of an estimator we analysed the versions of the ZZ estimator proposed in References 9-12. We found that the original ZZ-SPR proposed in References 4-7 is the most robust one, among the various versions tested, and some of the proposed ‘enhancements’ can lead to a significant deterioration of the asymptotic robustness of the estimator. From the analyses given in References 1-3 and in this paper, we found that the original ZZ estimator (given in References 4-7) is the most robust among all estimators analysed in References 1-3 and in this study. © 1997 John Wiley & Sons, Ltd.
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    An algebraically partitioned FETI method for parallel structural analysis: algorithm description (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2717-2737 
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    ISSN: 0029-5981
    Keywords: parallel computation ; algebraic partitioning ; domain decomposition ; structural analysis ; finite element method ; iterative solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algebraically partitioned FETI method for the solution of structural engineering problems on parallel computers is presented. The present algorithm consists of three attributes: an explicit generation of the orthogonal null-space matrix associated with the interface nodal forces, the floating subdomain rigid-body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized. Comparisons of the present method with the previously developed differentially partitioned FETI method are offered in terms of the saddle-point formulations at the end of the paper. A companion paper reports implementation details and numerical performance of the proposed algorithm. © 1997 John Wiley & Sons, Ltd.
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    SIMULTANEOUS OPTIMIZATION OF SHAPE AND FLOW PARAMETERS FOR COMBINED FREE AND FORCED CONVECTION IN VERTICAL CHANNELS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 551-563 
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    ISSN: 0029-5981
    Keywords: sensitivity analysis ; simultaneous optimization ; mixed convection ; finite element method ; material derivative concept ; adjoint variable method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simultaneous optimization of shape and flow parameters is performed for a combined free and forced convection flow through vertical rectangular channels with moving walls. The laminar flow is assumed to be fully developed in the axial direction. The wall velocity, the axial pressure gradient and the channel height in the transverse plane are taken as the optimization parameters. The sensitivity expressions of both the objective function and the flow rate constraint of optimization are obtained in terms of the relevant physical variables, as well as adjoint variables which satisfy additional p.d.e.'s. All equations are discretized using the finite element method. Numerical results are provided for the present constrained optimization problem for various values of the problem parameters which include the moving wall segment size and the Rayleigh number. The results indicate that with increased Rayleigh number the optimal values of the wall velocity and the axial pressure gradient are increased, while the optimal value of the channel height is decreased. General sensitivity expressions are also presented in the appendix which might be utilized for arbitrary boundary variations along with arbitrary optimization objectives in other investigations. © 1997 by John Wiley & Sons, Ltd.
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    A posteriori error estimation for finite element solutions of Helmholtz' equation - Part II: estimation of the pollution error (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3883-3900 
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    ISSN: 0029-5981
    Keywords: finite element method ; Helmholtz equation ; a posteriori error estimation ; acoustic scattering ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In part I of this investigation, we proved that the standard a posteriori estimates, based only on local computations, may severely underestimate the exact error for the classes of wave-numbers and the types of meshes employed in engineering analyses. We showed that this is due to the fact that the local estimators do not measure the pollution effect inherent to the FE-solutions of Helmholtz' equation with large wavenumber. Here, we construct a posteriori estimates of the pollution error. We demonstrate that these estimates are reliable and can be used to correct the standard a posteriori error estimates in any patch of elements of interest. © 1997 John Wiley & Sons, Ltd.
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    Two stress update algorithms for large strains: accuracy analysis and numerical implementation (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4363-4404 
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    ISSN: 0029-5981
    Keywords: large strains ; stress update ; error analysis ; convected frames ; nonlinear computational mechanics ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis. © 1997 John Wiley & Sons, Ltd.
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    MULTILEVEL AGGREGATION METHOD FOR SOLVING LARGE-SCALE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 453-471 
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    ISSN: 0029-5981
    Keywords: multi-level method ; aggregation method ; large scale problems ; finite element method ; structural dynamics ; generalized eigen value problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a novel iterative method of multilevel type for solving large-scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modification of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low-frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems. Numerical experiments performed for three-dimensional truss, frame and solid structures demonstrate an excellent performance of the method. © 1997 by John Wiley & Sons, Ltd.
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    A NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF VEHICLES MOVING ON FLEXIBLE STRUCTURES HAVING GAPS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 511-531 
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    ISSN: 0029-5981
    Keywords: dynamic contact ; multibody dynamics ; kinematic constraint ; vehicle ; flexible structure ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the dynamic analysis of vehicles moving on flexible structures which contain gaps. The Lagrange multipliers associated with the kinematic constraints of the vehicle components and the contact forces between the rigid wheels of the vehicle and the flexible structures are simultaneously computed with the solutions of the equations of motion by using the iterative schemes. On the kinematic joints and on the possible contact points the velocity and acceleration constraints as well as the displacement constraints are satisfied by the monotone reductions of the corresponding error vectors. And a well-developed simple one-step time integration of ordinary differential equation is employed for the solution of the equations of motion. Convergences of the iterative schemes are analysed and numerical simulations are conducted. © 1997 by John Wiley & Sons, Ltd.
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    EXTENSION OF THE ZIENKIEWICZ-ZHU ERROR ESTIMATOR TO SHAPE SENSITIVITY ANALYSIS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1413-1433 
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    ISSN: 0029-5981
    Keywords: finite element method ; adaptive refinement ; shape sensitivity analysis ; error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the Zienkiewicz-Zhu estimator was extended to the estimation of the discretization error arising from shape sensitivity analysis using the finite element method. The sensitivity error was quantified from the sensitivity of the energy norm by using an estimator specially developed for this purpose. Sensitivity analyses were carried out using the discrete analytical approach, which introduced no additional errors other than the discretization error. In this work, direct nodal averaging was used for linear triangular elements and the SPR technique for quadratic elements in order to obtain the smoothed stress and sensitivities fields. Two examples with an exact solution are used to analyse the effectivity of the proposed estimator and its convergence with the h-adaptive refinement. © 1997 by John Wiley & Sons, Ltd.
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    A higher-order facet quadrilateral composite shell element (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4477-4499 
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    ISSN: 0029-5981
    Keywords: shell element ; higher-order theory ; facet composite shell element ; flat shell element ; finite element method ; shear deformable flat shell element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A C0 finite element formulation of flat faceted element based on a higher-order displacement model is presented for the analysis of general, thin-to-thick, fibre reinforced composite laminated plates and shells. This theory incorporates a realistic non-linear variation of displacements through the shell thickness, and eliminates the use of shear correction coefficients. The discrete element chosen is a nine-noded quadrilateral with five and nine degrees of freedom per node.A comparison of results is also made with the 2-D thin classical and 3-D exact analytical results, and finite element solutions with 9-noded first-order element. © 1997 John Wiley & Sons, Ltd.
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    IMPROVED ENHANCED STRAIN FOUR-NODE ELEMENT WITH TAYLOR EXPANSION OF THE SHAPE FUNCTIONS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 407-421 
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    ISSN: 0029-5981
    Keywords: finite element method ; enhanced strain method ; symbolic integration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of enhanced strain four-node elements with Taylor expansion of the shape function derivatives is presented. A new concept of enhancement using besides the ‘standard’ enhanced strain fields also two other enhanced fields is developed on the basis of the Hu-Washizu principle. For first-order Taylor expansion enhanced modes become uncoupled, thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed. Furthermore, the formulation permits a symbolic integration, which leads to a closed-form solution for the element tangent matrix. Several numerical examples show that the element is stable, invariant, passes the patch test and yields good results especially in the highly distorted regime. © 1997 by John Wiley & Sons, Ltd.
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    A FINITE ELEMENT TECHNIQUE TO SIMULATE THE STABLE SHAPE EVOLUTION OF PLANAR CRACKS WITH AN APPLICATION TO A SEMI-ELLIPTICAL SURFACE CRACK IN A BIMATERIAL FINITE SOLID (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 905-917 
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    ISSN: 0029-5981
    Keywords: linear elastic fracture mechanics ; finite element method ; stress intensity factor ; energy release rate ; three-dimensional crack growth ; composite materials ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical procedure to model the crack front evolution of initially arbitrary shaped planar cracks in a three-dimensional solid. The influence of a bimaterial interface on the fracture path of a semi-elliptical surface crack in a three-dimensional structure is examined. The analysis is based on the assumption that fracture is controlled by small-scale yielding and linear elastic fracture mechanics. The finite element method and the crack-tip contour J-integral in a volume domain representation are utilized to calculate the crack front energy release rate. The computed values of the energy release rate are used with a crack-tip velocity growth law to model crack growth increment. The progress of the crack growth evolution is brought forward by successive iterations. Examples of computed crack evolution are given for an embedded circular crack, a semi-elliptical surface crack in a finite plate, and a configuration that defines an isotropic homogeneous material layer with a surface crack located between two material layers. © 1997 by John Wiley & Sons, Ltd.
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    FINITE ELEMENT SOLUTION OF A MODEL FREE SURFACE PROBLEM BY THE OPTIMAL SHAPE DESIGN APPROACH (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1525-1550 
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    ISSN: 0029-5981
    Keywords: adjoint problem ; discrete curvature ; finite element method ; free surface flow ; optimization ; quasi-Newton method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.
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    A THREE-DIMENSIONAL FINITE ELEMENT FORMULATION FOR THERMOVISCOELASTIC ORTHOTROPIC MEDIA (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2267-2288 
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    ISSN: 0029-5981
    Keywords: finite element method ; viscoelasticity ; incremental constitutive law ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the finite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the finite element solution. Use is made of a Dirichlet-Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. © 1997 John Wiley & Sons, Ltd.
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    A block solver for large, unsymmetric, sparse, banded matrices with symmetric profiles (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3279-3295 
    Details
    ISSN: 0029-5981
    Keywords: block solver ; unsymmetric matrix ; sparse ; banded ; linear equations ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A block equation solver for the solution of large, sparse, banded unsymmetric system of linear equations is presented in this paper. The method employs Crout variation of Gauss elimination technique for the solution. The solver ensures the efficient use of the available memory by doing block factorization and storage. It uses a skyline storage scheme which will avoid unnecessary operations on zero elements above the skyline which has found widespread use in banded symmetric solvers. A FORTRAN code with ample comments is provided. © 1997 John Wiley & Sons, Ltd.
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    A posteriori error estimation for finite element solutions of Helmholtz’ equation. part I: the quality of local indicators and estimators (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3443-3462 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; Helmholtz equation ; a posteriori error estimation ; acoustic scattering ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper contains a first systematic analysis of a posteriori estimation for finite element solutions of the Helmholtz equation. In this first part, it is shown that the standard a posteriori estimates, based only on local computations, severely underestimate the exact error for the classes of wave numbers and the types of meshes employed in engineering analysis. This underestimation can be explained by observing that the standard error estimators cannot detect one component of the error, the pollution error, which is very significant at high wave numbers. Here, a rigorous analysis is carried out on a one-dimensional model problem. The analytical results for the residual estimator are illustrated and further investigated by numerical evaluation both for a residual estimator and for the ZZ-estimator based on smoothening. In the second part, reliable a posteriori estimators of the pollution error will be constructed. © 1997 by John Wiley & Sons, Ltd.
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    Mass matrices by minimization of modal errors (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4259-4271 
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    ISSN: 0029-5981
    Keywords: finite element method ; mass matrix ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to constructing mass matrices is presented, based on expressing it through use of a variable parameter. This allows the mass matrix to be adjusted in such a way that a simple eigenvalue problem get the best solution possible in terms of some error measure. This procedure is used to create both diagonal mass matrices and mixed mass matrices. © 1997 John Wiley & Sons, Ltd.
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    A FINITE ELEMENT PERTURBATION METHOD FOR COMPUTING FLUID-INDUCED FORCES ON A CENTRIFUGAL IMPELLER ROTATING AND WHIRLING IN A VOLUTE CASING (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 269-294 
    Details
    ISSN: 0029-5981
    Keywords: centrifugal pumps ; potential fluid flow ; unsteady flow ; fluid forces ; finite element method ; perturbation analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element based method has been developed for computing time-averaged fluid-induced radial excitation forces and rotor dynamic forces on a two-dimensional centrifugal impeller rotating and whirling in a volute casing. In this method potential flow theory is used, which implies the assumption of irrotational inviscid flow. In comparison with other analyses of fluid-induced impeller forces, two main features have been included. Firstly, the hydrodynamic interaction between impeller and volute isproperly modelled. Secondly, the variation of the width of the volute has been adequately included in the two-dimensional analysis by a modification of the equation of continuity. A regular perturbation method is used to deal with the effects of the whirling motion of the impeller. The excitation forces are calculated from the zeroth-order problem in which the impeller axis is placed at the volute origin. The rotor dynamic forces associated with the whirling motion of the impeller are derived from the first-order solution. The force components, tangential and normal to the whirl orbit, are predicted as functions of the impeller--volute geometry, the flow conditions and the whirl speed ratio. The method is applied to a centrifugal pump experimentally tested at the California Institute of Technology. Comparisons between predictions and experimental data show the capabilities of the proposed method to reproduce the main features of fluid-induced impeller forces in centrifugal pumps. © 1997 by John Wiley & Sons, Ltd.
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    COMPARISON OF SENSITIVITY EQUATION AND ADJOINT EQUATION METHODS FOR PARAMETER IDENTIFICATION PROBLEMS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1015-1024 
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    ISSN: 0029-5981
    Keywords: parameter identification ; thermal conduction ; sensitivity equation ; adjoint equation ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the inverse analysis of a thermal conduction problem, in which the thermal conductivity is identified as an unknown parameter, which is determined so as to minimize the cost function represented by the square of the difference between the computed and observed temperatures at pre-assigned observation points. To minimize the cost function, both sensitivity equation and adjoint equation methods can be adopted. The sensitivity equation can be introduced by differentiating the governing equation directly. The sensitivity coefficient is obtained by the sensitivity equation. The adjoint equation is introduced via a variational approach using a Lagrange multiplier. The Lagrange multiplier is solution to an adjoint equation. Both sensitivity coefficient and Lagrange multiplier are used to calculate the gradient of the cost function. The purpose of this paper is to compare the sensitivity equation and adjoint equation methods from the convergence and computational efficiency points of view. © 1997 by John Wiley & Sons, Ltd.
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    An algebraically partitioned FETI method for parallel structural analysis: performance evaluation (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2739-2758 
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    ISSN: 0029-5981
    Keywords: parallel computation ; algebraic partitioning ; domain decomposition ; structural analysis ; finite element method ; iterative solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the algorithmic performance of an algebraically partitioned Finite Element Tearing and Interconnection (FETI) method presented in a companion paper. A simple structural assembly topology is employed to illustrate the implementation steps in a Matlab software environment. Numerical results indicate that the method is scalable, provided the iterative solution preconditioner employs the reduced interface Dirichlet preconditioner. A limited comparison of the present method with the differentially partitioned FETI method with corner modes is also offered. Based on this comparison and a reasonable extrapolation, we conclude the present algebraically partitioned FETI method possesses a similar iteration convergence property of the differentially partitioned FETI method with corner modes. © 1997 John Wiley & Sons, Ltd.
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    Analysis of finite element approximation and quadrature of Volterra integral equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 663-672 
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    ISSN: 0749-159X
    Keywords: finite element method ; Volterra integral equations ; Galerkin method ; projection method ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we study Galerkin finite element approximations to integral equations of the Volterra type. Our prime concern is the noncoercive case, which is not covered by the standard finite element theory. The question of rates of convergence is studied for the case where an exact stiffness matrix is available, as well as the case where the latter is approximated via quadrature rules. The optimality of these rules is also considered from the point of view of the effect the choice of the quadrature has on the overall rate of convergence. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 663-672, 1997
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    Towards adaptive finite element schemes for partial differential Volterra equation solvers (1996)
    Springer
    Advances in computational mathematics 6 (1996), S. 309-323 
    Details
    ISSN: 1572-9044
    Keywords: finite element method ; discontinuous Galerkin method ; a posteriori error estimates ; adaptivity ; Volterra equations ; viscoelasticity ; 45K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a brief indication of how elliptic, parabolic and hyperbolic partial differential equations with memory arise when modelling viscoelastic materials. We then point out the urgent need for adaptive solvers for these problems and, employing the methodology of Eriksson, Johnson et al. (e.g., SIAM J. Numer. Anal. 28 (1991)), we given ana posteriori error estimate for a model two-point hereditary boundary value problem. The strengths and weaknesses of the analysis and estimate are discussed.
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    Analysis of discrete techniques for image transformation (1996)
    Springer
    Numerical algorithms 13 (1996), S. 225-263 
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    ISSN: 1572-9265
    Keywords: numerical integration ; error analysis ; harmonic transformation ; finite element method ; digital image ; image transformation ; 65N15 ; 65D30 ; 68A45
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Let an image be distorted by a nonlinear transformationT, and then be restored back to its original by the inverse transformationT −1. Such a cycle conversion,T −1 T, of digital images can be facilitated by the combination (CSIM) given in [6] using the splitting-shooting method and the splitting-integrating method forT andT −1 respectively. Since there is no need to solve nonlinear equations, CSIM has been widely applied to specific areas of image processing and pattern recognition, even those with complicated transformations, e.g., the harmonic transformation [12]; however, no strict error analysis has been provided so far. In this paper, a priori error estimates and convergence rates are derived for pixel greyness obtained from CSIM; also the analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.
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    Free boundary problem of the 2D seepage flow (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 549-554 
    Details
    ISSN: 1573-2754
    Keywords: seepage flow ; variational inequality ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The free boundary of the seepage flow is a problem of close consideration in engineering. So far, an estimation of the wet set region usually needs a priori before the numerical analysis, and the configuration of the free boundary is then obtained by successive approximation. The authors of this paper benefit from a new mathematical expression—The Variational Inequality—to formulate the free boundary problem, which is then solved by the finite element method. Instead of the conventional way of discretization, here the finite element mesh is generated in the entire domain of the studied media and the free boundary of the seepage region can be defined directly without any process of iteration. The investigation gives a new effective scheme for the seepage flow analysis.
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    A study of the elasto-plastic axially tensile properties of metal matrix composites with fiber-end debonding (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 723-727 
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    ISSN: 1573-2754
    Keywords: debonding ; metal matrix composites ; elastoplasticity ; generalized self-consistent method ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Based on the generalized self-consistent finite element iterative averaging method, this paper studied the effects of the fiber-end debonding on the axially tensile elasto-plastic properties of SiC whiskers reinforced Aluminium matrix composite for various cases of different fiber's aspect ratios and volume fractions. Compared with the cases of perfect interface, it could be concluded that the effects of fiber-end debonding will become weaker with the fiber aspect ratio increasing and greater as the fiber volume fraction increases.
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    Comparison of several mesh refinement strategies near edges (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; mesh refinement ; adaptivity ; singularities near edges ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with several refinement techniques of finite element meshes for treating elliptic boundary value problems in domains with re-entrant edges and corners. A priori mesh grading is explained, and it is combined with the well-known adaptive finite element method. For two representative examples the numerically determined error norms are recorded, and the different strategies are compared.
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    Three and four step least squares finite element schemes in the time domain (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
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    ISSN: 1069-8299
    Keywords: time integration ; finite element method ; least squares formulation ; multistep methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is A0-stable but inconsistent.
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    Adaptive procedure for approximating functions by continuous piecewise polynomials (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
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    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
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    Superconvergent patch recovery technique for the finite element method in acoustics (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
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    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
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    Accurate stress extraction for nearly incompressible materials by the displacement formulation of the p-version FEM (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    Details
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
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    Study of warping torsion of thin-walled beams with closed cross-section using macro-elements (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    Details
    ISSN: 1069-8299
    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for computing the deformation of thin-walled beams with closed cross-section under warping torsional loading is presented. In comparison to the classical theory (Umanski), the hypothesis of no deformation of the contour of the cross-section of the beam is maintained and the assumption of no distortion of the cross-section plane is modified. The new approach gives better results than the classical theory when both are compared to a standard finite element technique (using shell elements). The central idea of the new approach lies in the usage of a new finite element called a macro-element, which is especially well suited for thin-walled beam computations.
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    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - I. SHAPE OPTIMIZATION METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
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    THREE-DIMENSIONAL TRANSIENT MOLD COOLING ANALYSIS BASED ON GALERKIN FINITE ELEMENT FORMULATION WITH A MATRIX-FREE CONJUGATE GRADIENT TECHNIQUE (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
    Details
    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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    CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THE h-ADAPTIVE FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4039-4061 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; optimal mesh ; strategy ; refinement ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five Adaptive Modification Strategies (AMSs) are studied as means to obtain nearly optimal meshes using an adaptive finite element modelling system based on the h-version of the FEM. These strategies include the method traditionally seem in the literature as well as four additional methods. The five strategies are tested over five numerical examples, one of them producing convergence oscillations in one example. The principal characteristic of our system is that it permits the user to control certain parameters of the adaptive process, which contributes to an improvement in the results.
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    Eigenvalue extraction for large finite element models using a new conjugate gradient algorithm (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 77-83 
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    ISSN: 1069-8299
    Keywords: eigenvalue extraction ; conjugate gradient method ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.
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    A SPACE-TIME FINITE ELEMENT METHOD FOR THE EXTERIOR STRUCTURAL ACOUSTICS PROBLEM: TIME-DEPENDENT RADIATION BOUNDARY CONDITIONS IN TWO SPACE DIMENSIONS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space and time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time-dependent radiation boundary conditions, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the matrix problem emanating from the space-time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space-time method.
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    THE p-VERSION OF THE FINITE ELEMENT METHOD IN INCREMENTAL ELASTO-PLASTIC ANALYSIS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1859-1878 
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    ISSN: 0029-5981
    Keywords: p-version ; finite element method ; elasto-plasticity ; cold-working ; non-linear problems ; continuum mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Whereas the higher-order versions of the finite element method (p- and hp-versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. In this paper, we discuss which aspects of incremental elasto-plastic finite element analysis are particularly amenable to improvements by the p-version. These theoretical considerations are supported by several numerical experiments. First, we study an example for which an analytical solution is available. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared with the traditional h-version but also with respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-working lug - is presented which demonstrates how the modelling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.
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  • 94
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    A GENERALIZED NEWTON METHOD FOR HIGHER-ORDER FINITE ELEMENT APPROXIMATIONS IN NON-LINEAR ELASTICITY (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2635-2646 
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    ISSN: 0029-5981
    Keywords: non-linear elasticity ; finite element method ; Newton method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.
    Additional Material: 6 Ill.
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  • 95
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    CONSIDERATION OF AGING OF SHOTCRETE IN THE CONTEXT OF A 3-D VISCOPLASTIC MATERIAL MODEL (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3123-3143 
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    ISSN: 0029-5981
    Keywords: shotcrete ; finite element method ; viscoplasticity ; smeared cracking ; aging ; Rankine criterion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of the classical theory of viscoplasticity and its algorithmic formulation in the context of an operator split scheme is extended to account for the effect of aging. Within this framework, a 3-D multisurface constitutive model for shotcrete is proposed. A rotating-crack model based on the Rankine criterion is adopted in conjunction with a Drucker-Prager yield criterion for describing the mechanical behaviour of young concrete in the compressive regime. The model is suitable for the representation of the time-dependent behaviour of shotcrete including creep and the time dependence of strength and stiffness. A computationally effective return mapping scheme is achieved by formulating the material model in terms of the principal directions and transforming the obtained relations to global axes. Linearization of the return mapping algorithm yields the algorithmic tangent moduli.
    Additional Material: 5 Ill.
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  • 96
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    STRESS- AND ROTATION-BASED HIERARCHIC MODELS FOR LAMINATED COMPOSITES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2647-2671 
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    ISSN: 0029-5981
    Keywords: hierarchic models ; laminated composites ; stress-based formulation ; complementary energy ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubeke's dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed.
    Additional Material: 14 Ill.
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  • 97
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    DIRECT FORMULATION FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL GROUNDWATER POLLUTION MODELLING WITH A COMPARISON WITH CONVENTIONAL FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2575-2591 
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    ISSN: 0029-5981
    Keywords: finite element method ; numerical analysis ; numerical method ; groundwater modelling ; subsurface modelling ; groundwater pollution modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Real world ground water pollution modelling deals with solute transport through anisotropic, heterogeneous media. The applicability of analytical solutions for such a real world system is extremely limited. As an effective tool, numerical models, such as finite difference and finite element methods, are usually employed to model field scenarios. Nevertheless, ground water pollution modelling is a hallenging task and frequently ends up with misleading results. Most of the time insufficient data are blamed for such erratic results. A recent investigation shows that the shortcomings of numerical formulations may be the major cause for many disputes and confusions in numerical analyses. In reality, a point injection of water in a static, homogeneous and isotropic groundwater system shows a radial dissipation of water forming a sphere; and a full-depth line injection shows a radial dissipation forming a cylinder. The finite difference method completely ignores this fundamental flow principles and allows water only to flow along orthogonal directions. To overcome this limitation, the finite element method was developed as a flexible approach in order to connect a node with the neighbouring nodes in various directions where water is assumed to flow in any directions along node connections. In a recent investigation, it has been found that the conventional finite element method does not keep the commitments; and its formulation techniques lead to a global matrix where a solution domain is not connected with all the neighbouring nodes and does not comply with the control-volume mass balance concept. A consistent finite element formulation approach which does not need imaginary mathematical formulation and overcomes the limitations of both the conventional finite difference and finite element methods has been developed. This method allows fluid flow and solute transport in a porous medium in radial directions. The global matrices for flow and transport obtained from this technique are field representative, diagonally dominant and easily convergent. The new method is robust, needs less mathematical computation and has many advantages over the conventional finite difference and finite element methods.
    Additional Material: 6 Ill.
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  • 98
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    GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3391-3403 
    Details
    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
    Additional Material: 8 Ill.
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  • 99
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    NUMERICAL ANALYSES OF TUNNEL LININGS BY MEANS OF A VISCOPLASTIC MATERIAL MODEL FOR SHOTCRETE (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3145-3162 
    Details
    ISSN: 0029-5981
    Keywords: shotcrete ; tunnelling ; cap model ; New Austrian Tunnelling Method (NATM) ; finite element method ; viscoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the parameter identification, verification and selected applications of a 3D viscoplastic material model for shotcrete proposed by Meschke. The performance of the shotcrete model is evaluated by means of reanalyses of short-term and creep tests on shotcrete specimen. The most essential items of a viscoplastic cap model used for the representation of soil including the determination of the model parameters are also presented. Both models are employed in a 3D finite element simulation of the excavation of a single-track tunnel driven according to the New Austrian Tunnelling Method. Comparisons between in situ measurements and numerical results are presented.
    Additional Material: 15 Ill.
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  • 100
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    AN IMPLICIT PROJECTION ALGORITHM FOR SIMULTANEOUS FLOW OF PLASTICITY AND DAMAGE IN STANDARD GENERALIZED MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3065-3082 
    Details
    ISSN: 0029-5981
    Keywords: biomechanics ; damage ; finite element method ; plasticity ; standard generalized material ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Motivated by mechanical analysis of cancellous bone, a 3D constitutive law describing the simultaneous flow of rate-independent plasticity and damage is developed in the framework of thermodynamics of irreversible processes with internal variables. Following the hypothesis of standard generalized materials, a free energy and a dissipation potential are postulated and the associated flow rules derived with the tools of convex analysis. On the computational side, the classical implicit projection (or catching up) algorithm used in plasticity is extended to account for the additional flow of damage. Due to the existence of a dissipation potential, linearization of the incremental algorithm provides a symmetric tangent operator. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the quadratic convergence of the algorithm.
    Additional Material: 10 Ill.
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