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  • 1
    Electronic Resource
    Electronic Resource
    On a certain two-sided symmetric condition in magnetic field analysis and computations (1997)
    Springer
    Applications of mathematics 42 (1997), S. 147-159 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022295111737
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  • 2
    Electronic Resource
    Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02127710
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  • 3
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023012328209
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  • 4
    Electronic Resource
    Electronic Resource
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Correction of finite element eigenvalues for problems with natural or periodic boundary conditions (1988)
    Springer
    BIT 28 (1988), S. 254-269 
    Details
    ISSN: 1572-9125
    Keywords: 65L15 ; 65L60 ; asymptotic correction ; Sturm-Liouville eigenvalues ; finite element method ; natural boundary conditions ; periodic boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recent results of Andrew and Paine for a regular Sturm-Liouville problem with essential boundary conditions are extended to problems with natural or periodic boundary conditions. These results show that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k 4 h 2) toO(kh 2). Numerical results show the correction to be useful even for low values ofk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934090
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  • 7
    Electronic Resource
    Electronic Resource
    A framework for advancing front techniques of finite element mesh generation (1995)
    Springer
    BIT 35 (1995), S. 210-232 
    Details
    ISSN: 1572-9125
    Keywords: Unstructured meshes ; finite element method ; Delaunay triangulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Advancing front techniques are a family of methods for finite element mesh generation that are particularly effective in dealing with complicated boundary geometries. In the first part of this paper, conditions are presented which ensure that any planar aft algorithm that meets these conditions terminates in a finite number of steps with a valid triangulation of the input domain. These conditions are described by specifying a framework of subtasks that can accommodate many aft methods and by prescribing the minimal requirements on each subtask that ensure correctness of an algorithm that conforms to the framework. An important efficiency factor in implementing an aft is the data structure used to represent the unmeshed regions during the execution of the algorithm. In the second part of the paper, we discuss the use of the constrained Delaunay triangulation as an efficient abstract data structure for the unmeshed regions. We indicate how the correctness conditions of the first part of the paper can be met using this representation. In this case, we also discuss the additional requirements on the framework which ensure that the generated mesh is a constrained Delaunay triangulation for the original boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01737163
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  • 8
    Electronic Resource
    Electronic Resource
    Ultrasonic beam propagation through a bimetallic weld—A comparison of predictions of the Gauss-Hermite beam model and finite element method (1993)
    Springer
    Journal of nondestructive evaluation 12 (1993), S. 151-158 
    Details
    ISSN: 1573-4862
    Keywords: Beam propagation ; bimetallic weld ; Gauss-Hermite beam model ; finite element method ; ultrasonics ; anisotropic medium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract In this paper, predictions of two models for the propagation of ultrasonic beams through a two-dimensional, bimetallic weld geometry are compared. The finite element method can predict beam propagation through quite general geometry with high accuracy. This model, however, requires significant computational time. On the other hand, the approximate Gauss-Hermite model offers considerably greater computational speed, but has lower accuracy in certain regions and cannot treat the most general geometries and inhomogeneities in material properties. This paper compares the performances of the two models for the case of the two-dimensional, bimetallic weld consisting of multiple layers, some of which have anisotropic properties. It is found that the results of the two models are in good agreement in the vicinity of the central ray, and that the deviation increases as one moves away from the axis. Also, as the beam propagates through multiple interfaces, the accuracy of the Gauss-Hermite solution decreases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00567571
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  • 9
    Electronic Resource
    Electronic Resource
    Identification of crack size via an energy approach (1994)
    Springer
    Journal of nondestructive evaluation 13 (1994), S. 1-11 
    Details
    ISSN: 1573-4862
    Keywords: Crack detection ; modal testing ; nondestructive evaluation ; fracture mechanics ; structure ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract An energy method for identifying the size of a crack at given location in structures using one measured eigencouple of the cracked structures is presented. The method utilizes the maximum strain energies of the structures both with and without a crack and the additional strain energy induced by the crack to construct the energy balance equation from which the size of the crack is evaluated through an iteration procedure. A pair of measured vibration frequency and mode shape of the cracked structure is used in a free vibration analysis to derive for its maximum strain energy. The maximum inertia force of the cracked structure is then applied to the uncracked structure with known stiffness and the resulting strain energy of the uncracked structure is obtained in a finite element analysis. Fracture mechanics is used to derive for the additional strain energy induced by the crack. Experimental investigations of several cracked free-free beams are performed to validate the proposed method. Examples of the identification of crack sizes for a number of damaged beam structures are given to further illustrate the feasibility and effectiveness of the present method. Overall the results are encouraging showing that the present method has the prospect of becoming an alternative approach for crack size detection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00723942
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  • 10
    Electronic Resource
    Electronic Resource
    Analysis of discrete techniques for image transformation (1996)
    Springer
    Numerical algorithms 13 (1996), S. 225-263 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02207696
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  • 11
    Electronic Resource
    Electronic Resource
    Numerical bifurcation and stability analysis for steady-states of reaction diffusion equations (1997)
    Springer
    Numerical algorithms 14 (1997), S. 211-225 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019117130906
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  • 12
    Electronic Resource
    Electronic Resource
    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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  • 13
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    Evanescent energy in square and circular fibers (2000)
    Springer
    Journal of mathematical chemistry 27 (2000), S. 251-265 
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    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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  • 14
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    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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  • 15
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    Buckling and post-buckling of annular plates under non-axisymmetric plane edge forces (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 469-480 
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    ISSN: 1573-2754
    Keywords: non-axisymmetric edge forces ; variational principle ; finite element method ; post-buckling behaviour
    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 both the general theory [1,2] and the finite element method [4] of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02019592
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  • 16
    Electronic Resource
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    Criteria for finite element algorithm of generalized heat conduction equation (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 587-596 
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    ISSN: 1573-2754
    Keywords: heat conduction equation ; hyperbolic differential equation ; finite element method ; criteria ; oscillation ; overbounding
    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 To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized heat conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02451522
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  • 17
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    Finite element analysis for the unsteady nearshore circulation due to wave-current interaction (II) — Two-step explicit finite element method (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 841-848 
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    ISSN: 1573-2754
    Keywords: finite element method ; unsteady circulation ; vortex
    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, the two-step explicit finite element analysis for the numerical model of the unsteady nearshore circulation proposed in·Ref. [1] and its realization of Fortran program are presented. A circulation has been, clearly shown in the calculated wave-current velocity field, and it is in good agreement with observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02451633
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  • 18
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    The random variational principle and finite element method (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 401-406 
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    ISSN: 1573-2754
    Keywords: variational principle ; finite element method ; perturbation 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 In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method. Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02450730
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  • 19
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    Numerical residual elimination method of finite differential equations (1993)
    Springer
    Applied mathematics and mechanics 14 (1993), S. 185-191 
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    ISSN: 1573-2754
    Keywords: finite differential method ; finite element method ; residual equations ; direct iteration
    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 elimination of finite differential equations has been discussed. It applies the numerical direct iteration to obtain the residual equations, in which the number of unknowns has been reduced greatly. The solution process is simple and efficient, and the solution is exact
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02453361
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  • 20
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    Mixed compatible element and mixed hybrid incompatible element variational methods in dynamics of viscous barotropic fluids (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 561-569 
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    ISSN: 1573-2754
    Keywords: mechanics of viscous fluids ; computational fluid mechanics ; variational principle ; finite element method ; mixed compatible element ; mixed hybrid incompatible element
    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 and proves the mixed compatible finite element variational principles in dynamics of viscous barotropic fluids. When the principles are proved, it is found that the compatibility conditions of stress can be naturally satisfied. The generalized variational principles with mixed hybrid incompatible finite elements are also presented and proved, and they can reduce the computation of incompatible elements in dynamics of viscous barotropic flows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02450769
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  • 21
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    Free boundary problem of the 2D seepage flow (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 549-554 
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    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00119752
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  • 22
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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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    URL: http://dx.doi.org/10.1007/BF00189560
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  • 23
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02457502
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  • 24
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00127014
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  • 25
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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 
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    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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    Finite element analysis for consolidation in interaction between structure and saturated soil foundation (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 929-937 
    Details
    ISSN: 1573-2754
    Keywords: finite element method ; consolidation/interaction
    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 consolidation analysis of interaction between structure and saturated soil foundation is discussed. With the use of substructure technique, the structure is condensed onto the interface of the soil, and then the consolidation governing equations to describe the interaction between soil and structure are derived. The solution with non-iterative algorithm is proposed in this paper. The pressure Master-Slave relation method is used to deal with the non-permeability conditions on soil boundaries. A numerical example is illustrated. Based on this paper, the interactive consolidation analysis between large structure and soil has been more practical.
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    URL: http://dx.doi.org/10.1007/BF02453335
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    The random variational principle in finite deformation of elasticity and finite element method (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 903-911 
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    ISSN: 1573-2754
    Keywords: finite deformation ; variational principle ; finite element method ; structural reliability analysis
    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 the present paper, we have introduced the random materials, toads, geometrical shapes, force and displacement boundary condition directly into the functional variational formula, by use of a small parameter perturbation method, a unified random variational principle in finite deformation of elasticity and nonlinear random finite element method are established, and used for reliability analysis of structures. Numberical examples showed that the methods have the advantages of simple and conveninet program implementation and are effective for the probabilistic problems in mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02451033
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    Transient analysis of artificial mechanical valve-blood interaction (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 437-442 
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    ISSN: 1573-2754
    Keywords: artificial mechanical value ; fluid-solid interaction ; transient dynamic analysis ; 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 Using finite element method, this paper has analyzed the blood-mechanical heart valve interaction system subjected to a step pressure when the value is, at closing position. As demonstrated in the present study, in, such conditions mechanical values made of pyrolytic carbon, Ti alloy, Co-Cr alloy and ceramics tend to be very stiff which result in high impinging pressure. The impinging pressure acted on the value of the blood-valve system can be reduced by decreasing the elastic modulus of the mechanical value.
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    URL: http://dx.doi.org/10.1007/BF02459342
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    Finite element analysis of wave propagation in fluid-saturated porous media (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 1331-1341 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02459166
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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 
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    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.
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    URL: http://dx.doi.org/10.1023/A:1008375006703
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    Numerical Methods for Accurate Computation of Design Sensitivities for Two-Dimensional Navier-Stokes Problems (2000)
    Springer
    Optimization and engineering 1 (2000), S. 277-304 
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    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.
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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.
    Additional Material: 5 Ill.
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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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    On vibration of hemispherical shell by using finite element method (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 1169-1175 
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    ISSN: 1573-2754
    Keywords: hemispherical shell ; vibration ; finite element method ; resonant frequency
    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 establishes the finite element equation for the spherical shell. The resonant frequencies of the above shell under different boundary conditions are also discussed and calculated.
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    Spectral-finite element method for compressible fluid flow (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 701-717 
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    ISSN: 1573-2754
    Keywords: compressible fluid flow ; spectral method ; finite element method ; error estimation
    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 combined Fourier spectral-finite element method is proposed for solving n-dimensional (n=2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.
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    3-D numerical study on the bending of symmetric composite laminates (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 1-6 
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    ISSN: 1573-2754
    Keywords: composite ; laminate ; plate stress analysis ; finite element method ; three dimension ; interlaminar surface ; stress concentration
    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, the composite, laminates subjected to pure bending are modelled by using 3-D anisotropic finite elements and the distributions of stress and strain along the thickness are presented. The numerical results show that there is a stress concentration near the bonding interface in the central region (far from traction boundaries and free edges) of symmetric angle-ply laminates, which should be called “interlaminar effect”. The abrupt change of the mechanical behavior of material on the interfaces causes interlaminar stresses. The laminates are in 3-D stress state near the interfaces. The strain distribution of the 3-D numerical model is different from the strain hypothesis of the classical laminate theory based on the Kirchhoff-Love hypotheses of straight inextensional normals.
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    Finite element analysis for the unsteady nearshore circulation due to wave-current interaction (I)—numerical model (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 749-754 
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    ISSN: 1573-2754
    Keywords: numerical model ; finite element method ; unsteady circulation ; nearshore circulation
    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 numerical model for predicting the unsteady nearshore circulation due to wave-current interaction was proposed. In addition to the traditional continuity, momentum and energy equations, the dispersion and refraction relations were included in the governing equations. Moreover, the effects of lateral shears, wind, radiation and bottom stresses were analysed in the governing equations. Therefore, we expect that this model may more completely and exactly reflect the law of wave-current interaction. In part (II) we will adopt the selective lumping two-step explicit finite element method to solve the model, and some examples will be presented.
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    Comprehensive mathematical model of microcirculatory dynamics (II)—Calculation and the results (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 579-584 
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    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.
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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.
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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 
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    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.
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    A new method for stress analysis of a cyclically symmetric structure (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 87-94 
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    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.
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    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 
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    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.
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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 
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    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.
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    An iterative parallel algorithm of finite element method (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 305-313 
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    ISSN: 1573-2754
    Keywords: parallel algorithm ; finite element method ; iterative solution ; weighted residual 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 In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.
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    A modification of Taylor-Galerkin Finite Element Method and its application (1993)
    Springer
    Applied mathematics and mechanics 14 (1993), S. 1173-1179 
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    ISSN: 1573-2754
    Keywords: hypothesis ; finite element method ; stream function iteration
    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 Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.
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    The finite element method based on interpolating with wavelet basis function (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 13-18 
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    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.
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    On numerical solution of hemivariational inequalities by nonsmooth optimization methods (1995)
    Springer
    Journal of global optimization 6 (1995), S. 401-425 
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    ISSN: 1573-2916
    Keywords: hemivariational inequalities ; finite element method ; substationary point ; nonsmooth optimization ; bundle methods ; nonmonotone contact problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider numerical solution of hemivariational inequalities (HVI) by using nonsmooth, nonconvex optimization methods. First we introduce a finite element approximation of (HVI) and show that it can be transformed to a problem of finding a substationary point of the corresponding potential function. Then we introduce a proximal budle method for nonsmooth nonconvex and constrained optimization. Numerical results of a nonmonotone contact problem obtained by the developed methods are also presented.
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    Dynamic modeling of a revolute-prismatic flexible robot arm fabricated from advanced composite materials (1991)
    Springer
    Nonlinear dynamics 2 (1991), S. 171-186 
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    ISSN: 1573-269X
    Keywords: Flexible robotic manipulator ; advanced composites ; mathematical modeling ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dynamic model for a two degree-of-freedom planar robot arm is derived in this study. The links of the arm, connected to prismatic and revolute joints, are considered to be flexible. They are assumed to be fabricated from either aluminum or laminated composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. These effects are significant in modeling flexible links connected to prismatic joints. The deflections of the links are approximated by using a shear-deformable beam finite element. Hamilton's principle is implemented to derive the equations describing the combined rigid and flexible motions of the arm. The resulting equations are coupled and highly nonlinear. In view of the large number of equations involved and their geometric nonlinearity (topological and quadratic), the solution of the equations of motion is obtained numerically by using a stiff integrator. The digital simulation studies examine the interaction between the flexible and the rigid body motions of the robot arm, investigate the improvement in the accuracy of the model by considering the flexibility of all rather than some of the links of the arm, assess the significance of the rotary inertia and shear deformation, and illustrate the advantages of using advanced composites in the structural design of robotic manipulators.
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    An eight noded composite plate element for the dynamic analysis of spatial mechanism systems (1994)
    Springer
    Nonlinear dynamics 5 (1994), S. 459-476 
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    ISSN: 1573-269X
    Keywords: Composite plates ; nonlinear vibration ; finite element method ; multibody dynamics ; stress analysis ; and numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The development of a shear-deformable laminated plate element, based on the Mindlin plate theory, for use in large reference displacement analysis is presented. The element is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotrophic material property sets. Coordinate mapping is utilized so that non-rectangular elements may be modeled. The Gauss quadrature method of numerical integration is utilized to evaluate volume integrals. A comparative study is done on the use of full Gauss quadrature, reduced Gauss quadrature, mixed Gauss quadrature, and closed form integration techniques for the element. Dynamic analysis is performed on the RSSR (Revolute-Spherical-Spherical-Revolute) mechanism, with the coupler modeled as a flexible plate. The results indicate the differences in the dynamic response of the transverse shear deformable eight-noded element as compared to a four-noded plate element. Dynamically induced stresses are examined, with the results indicating that the primary deformation mode of the eight-noded Mindlin plate model being bending.
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    URL: http://dx.doi.org/10.1007/BF00052454
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    Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems (1994)
    Springer
    Nonlinear dynamics 6 (1994), S. 1-20 
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    ISSN: 1573-269X
    Keywords: Nonlinear dynamics ; control structure interaction ; multibody dynamics ; finite element method ; Lagrangian dynamics ; and inverse dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.
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    URL: http://dx.doi.org/10.1007/BF00045429
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    Control structure interaction in the nonlinear analysis of flexible mechanical systems (1993)
    Springer
    Nonlinear dynamics 4 (1993), S. 183-206 
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    ISSN: 1573-269X
    Keywords: Nonlinear dynamics ; control structure interaction ; multibody dynamics ; finite element method ; Lagrangian dynamics ; inverse dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The effect of the control structure interaction on the feedforward control law as well as the dynamics of flexible mechanical systems is examined in this investigation. An inverse dynamics procedure is developed for the analysis of the dynamic motion of interconnected rigid and flexible bodies. This method is used to examine the effect of the elastic deformation on the driving forces in flexible mechanical systems. The driving forces are expressed in terms of the specified motion trajectories and the deformations of the elastic members. The system equations of motion are formulated using Lagrange's equation. A finite element discretization of the flexible bodies is used to define the deformation degrees of freedom. The algebraic constraint equations that describe the motion trajectories and joint constraints between adjacent bodies are adjoined to the system differential equations of motion using the vector of Lagrange multipliers. A unique displacement field is then identified by imposing an appropriate set of reference conditions. The effect of the nonlinear centrifugal and Coriolis forces that depend on the body displacements and velocities are taken into consideration. A direct numerical integration method coupled with a Newton-Raphson algorithm is used to solve the resulting nonlinear differential and algebraic equations of motion. The formulation obtained for the flexible mechanical system is compared with the rigid body dynamic formulation. The effect of the sampling time, number of vibration modes, the viscous damping, and the selection of the constrained modes are examined. The results presented in this numerical study demonstrate that the use of the driving forees obtained using the rigid body analysis can lead to a significant error when these forces are used as the feedforward control law for the flexible mechanical system. The analysis presented in this investigation differs significantly from previously published work in many ways. It includes the effect of the structural flexibility on the centrifugal and Coriolis forces, it accounts for all inertia nonlinearities resulting from the coupling between the rigid body and elastic displacements, it uses a precise definition of the equipollent systems of forces in flexible body dynamics, it demonstrates the use of general purpose multibody computer codes in the feedforward control of flexible mechanical systems, and it demonstrates numerically the effect of the selected set of constrained modes on the feedforward control law.
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    URL: http://dx.doi.org/10.1007/BF00045253
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    Effect of the order of the finite element and selection of the constrained modes in deformable body dynamics (1992)
    Springer
    Nonlinear dynamics 3 (1992), S. 57-80 
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    ISSN: 1573-269X
    Keywords: Dynamics ; finite element method ; triangular elements ; multibody dynamics ; component mode synthesis ; nonlinear vibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Finite elements with different orders can be used in the analysis of constrained deformable bodies that undergo large rigid body displacements. The constrained mode shapes resulting from the use of finite elements with different orders differ in the way the stiffness of the body bending and extension are defined. The constrained modes also depend on the selection of the boundary conditions. Using the same type of finite element, different sets of boundary conditions lead to different sets of constrained modes. In this investigation, the effect of the order of the element as well as the selection of the constrained mode shapes is examined numerically. To this end, the constant strain three node triangular element and the quadratic six node triangular element are used. The results obtained using the three node triangular element are compared with the higher order six node triangular element. The equations of motion for the three and six node triangular elements are formulated from assumed linear and quadratic displacement fields, respectively. Both assumed displacement fields can describe large rigid body translational and rotational displacements. Consequently, the dynamic formulation presented in this investigation can also be used in the large deformation analysis. Using the finite element displacement field, the mass, stiffness, and inertia invariants of the three and six-node triangular elements are formulated. Standard finite element assembly techniques are used to formulate the differential equations of motion for mechanical systems consisting of interconnected deformable bodies. Using a multibody four bar mechanism, numerical results of the different elements and their respective performance are presented. These results indicate that the three node triangular element does not perform well in bending modes of deformation.
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    Modified calculation of the dissipation term in thermoplastic finite element equations (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
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    ISSN: 1069-8299
    Keywords: finite element method ; thermoplasticity ; internal dissipation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
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    URL: http://dx.doi.org/10.1002/cnm.1640110110
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    The variationally correct rate of convergence for a two-noded beam element, or why residual bending flexibility correction is an extravariational trick (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 403-407 
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    ISSN: 1069-8299
    Keywords: finite element method ; residual bending flexibility ; convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.
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    URL: http://dx.doi.org/10.1002/cnm.1640110504
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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 
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    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 
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    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 
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    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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    IMPROVING MODULARITY IN OBJECT-ORIENTED FINITE ELEMENT PROGRAMMING (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
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    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 
    Details
    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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    A posteriori error estimates and adaptivity for finite element solutions in finite elasticity (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 775-795 
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    ISSN: 0029-5981
    Keywords: computational mechanics ; finite element method ; a posteriori error estimation ; finite elasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods for a posteriori error estimation for finite element solutions are well established and widely used in engineering practice for linear boundary value problems. In contrast here we are concerned with finite elasticity and error estimation and adaptivity in this context. In the paper a brief outline of continuum theory of finite elasticity is first given. Using the residuals in the equilibrium conditions the discretization error of the finite element solution is estimated both locally and globally. The proposed error estimator is physically interpreted in the energy sense. We then present and discuss the convergence behaviour of the discretization error in uniformly and adaptively refined finite element sequences.
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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 
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    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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    Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3745-3774 
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    ISSN: 0029-5981
    Keywords: Helmholtz equation ; finite element method ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non-dispersive media. The numerical wave displays a phase velocity that depends on the parameter k of the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one-dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates in H1-norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximation p(h-p-version).
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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 
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    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 
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    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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    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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    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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    On understanding and teaching of the finite element method (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 105-115 
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    ISSN: 1069-8299
    Keywords: finite element method ; conceptual diagrams ; error estimation ; postprocessing ; teaching ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behaviour of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more.
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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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    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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    2D or 3D frictional contact algorithms and applications in a large deformation context (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 409-416 
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    ISSN: 1069-8299
    Keywords: contact ; friction ; finite element method ; large deformation ; augmented Lagrangian method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
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    An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 899-909 
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    ISSN: 1069-8299
    Keywords: finite element method ; non-linear shell elements ; assumed strain approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadrilateral degenerated C0 shell element is presented which relies on extensible director kinematics and which incorporates unmodified three-dimensional constitutive models. It is shown that the direct interpolation of the extensible director field causes severe locking behaviour in the case of thin shell structures. An assumed strain interpolation is proposed to overcome the thin-shell defect. Due to this modification the shell element is able to accommodate large rotations without a rotation tensor, even for very thin shells. Several large deformation examples confirm that the developed shell element is competitive with more elaborate formulations which use rotational degrees of freedom.
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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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    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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    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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    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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    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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    A semi-analytic method for dynamic response analysis based on Gurtin's variational principle (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 297-306 
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    ISSN: 1069-8299
    Keywords: semi-analytic method ; dynamic response ; convolution ; variational principle ; series ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency.
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    The new variational problem in three-dimensional eddy-current field computation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 727-733 
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    ISSN: 1069-8299
    Keywords: eddy currents ; finite element method ; equivalence ; uniqueness ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new variational problem corresponding to a three-dimensional eddy-current boundary-value problem is treated in the paper. The equivalence between the variational problem and the boundary-value problem is proved, and so is the uniqueness of the solution. These form the foundation of the H - Ψ method.
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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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    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 
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    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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    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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    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 
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    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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    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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    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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    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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  • 100
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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 
    Details
    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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