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  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
    ISSN: 0170-4214
    Keywords: gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 2
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
    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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  • 3
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
    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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  • 4
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 403-407 
    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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  • 5
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    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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  • 6
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
    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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  • 7
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    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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  • 8
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    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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  • 9
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    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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  • 10
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    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    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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  • 11
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
    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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  • 12
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 103-112 
    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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  • 13
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 319-326 
    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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  • 14
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    Communications in Numerical Methods in Engineering 13 (1997), S. 343-353 
    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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  • 15
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    Communications in Numerical Methods in Engineering 13 (1997), S. 355-372 
    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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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 775-795 
    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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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    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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  • 18
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3745-3774 
    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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  • 19
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
    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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  • 20
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4039-4061 
    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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  • 21
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    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
    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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  • 22
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    Communications in Numerical Methods in Engineering 13 (1997), S. 705-713 
    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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  • 23
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    Communications in Numerical Methods in Engineering 11 (1995), S. 105-115 
    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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  • 24
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    Communications in Numerical Methods in Engineering 14 (1998), S. 135-149 
    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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  • 25
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    Communications in Numerical Methods in Engineering 14 (1998), S. 181-194 
    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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  • 26
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    Communications in Numerical Methods in Engineering 11 (1995), S. 409-416 
    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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  • 27
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    Communications in Numerical Methods in Engineering 11 (1995), S. 899-909 
    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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    Communications in Numerical Methods in Engineering 12 (1996), S. 77-83 
    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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    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    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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    Communications in Numerical Methods in Engineering 14 (1998), S. 9-22 
    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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    Communications in Numerical Methods in Engineering 14 (1998), S. 997-1012 
    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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    Communications in Numerical Methods in Engineering 14 (1998), S. 1119-1131 
    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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  • 33
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    Communications in Numerical Methods in Engineering 11 (1995), S. 297-306 
    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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    Communications in Numerical Methods in Engineering 11 (1995), S. 727-733 
    ISSN: 1069-8299
    Keywords: eddy currents ; finite element method ; equivalence ; uniqueness ; Engineering ; Engineering General
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    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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    Journal of Computational Chemistry 17 (1996) 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Computer Science
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  • 36
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    Journal of Computational Chemistry 17 (1996), S. 289-297 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: In spite of much work on path-following methods, a solid mathematical foundation (especially convergence conditions and their practical measures) are lacking in most cases. In our previous articles the general theory of a new global searching procedure, the dynamically defined reaction path (DDRP) method, its rigorous mathematical formulation, the algorithm, a practical computation program, and some applications to abstract mathematical functions and simple chemical examples have been presented. In this article we give a short theoretical description and some practical criteria and measures for the convergence of the method and illustrate the principles and uses by numerical mathematical and chemical examples. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 298-305 
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    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Transition states for the Diels-Alder reactions of 2,3-diaza-1,3-butadiene with ethylene, formaldehyde, formaldimine, cis- and trans- diazene, and nitrosyl hydride were located by ab initio molecular orbital calculations. The bond orders of the new forming bonds have been used to determine the asynchronicity of the reactions. Ab initio calculations show that the energy barrier for the hetero-Diels-Alder reactions is relatively high. The highest energy barrier of 34.76 kcal/mol calculated at the MP4/6-31G*//MP2/6-31G* level was found for the exo-cis-diazene addition to 2,3-diaza-1,3-butadiene. In all cases, when two diastereomeric transition structures are possible, the one with the endo hydrogen, exo lone pair was predicted to have a lower activation barrier. This behavior can be explained by the n-π and n-n loan pair repulsion interaction between the dienophile and diene heteroatoms in the corresponding transition state. The barrier is higher for those reactions which in the transition state have more lone electron pairs. Also, the barrier is higher when the lone pairs are endo oriented than when they are exo oriented in the transition state. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 338-349 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Computer Science
    Notes: More than a dozen stationary points on the potential energy surface for the 1:1 glycine zwitterion - water complex have been investigated at Hartree-Fock or MP2 levels of theory with basis sets ranging from split valence (4-31G) to split valence plus polarization and diffuse function (6-31 + + G**) quality. Only one true minimum (GLYZWM, C1 symmetry) could be located on the potential energy surface. GLYZWM features a bridged water molecule acting as both a hydrogen bond acceptor and donor with the NH3- and CO2- units of the glycine zwitterion. The total hydrogen bond energy in GLYZWM is computed as 16 kcal/mol (MP2/6-31 ++ G** // 6-31 ++ G**, including corrections for basis set superpositions errors). The computed vibrational frequencies and normal mode forms of the GLYZWM complex resemble in many cases experimental assignments made for the glycine zwitterion in bulk water on the basis of Raman spectroscopy. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 386-395 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A combined ab initio quantum mechanical and molecular mechanical (AI-QM/MM) potential for use in molecular modeling and simulation has been described. In this article, we summarize a procedure for deriving the empirical parameters embedded in a combined QM/MM model and suggest a set of Lennard-Jones parameters for the combined ab initio 3-21G and MM OPLS-TIP3P (AI-3/MM) potential. Interaction energies and geometrical parameters predicted with the AI-3/MM model for over 80 hydrogen-bonded complexes of organic compounds with water were found to be in good accord with ab initio 6-31G(d) results. We anticipate that the AI-3/MM potential should be reasonable for use in condensed phase simulations. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 1-18 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Potential derived (PD) atomic charges, obtained by fitting to molecular electrostatic potentials, are widely used in molecular modeling and simulation calculations. These charges are known to depend on the sample of points chosen for the fit, on the particular point selection algorithm, on molecular translations and rotations in many instances, and even on molecular conformation. Following a critique of currently available methods, a novel point selection scheme is described which results in a highly isotropic array of points located on a series of fused-sphere van der Waals surfaces. The pattern of points is based on tesselations of the icosahedron, and these are discussed in some detail along with their connection with virus morphology, geodesic domes, and symmetric fullerene structures. Using methanol as a test case, it is shown that the new method leads to PD charges which are independent of translation and display minimal rotational dependence, and are hence far better suited to the determination of PD charges from electrostatic potentials obtained from both theory and experimental X-ray diffraction data. The conformation dependence of the newly derived PD charges for alanyl dipeptide is found to be substantially less than obtained earlier by Williams [Biopolymers 29, 1367 (1990)]. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996) 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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  • 42
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    Journal of Computational Chemistry 17 (1996), S. 757-766 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Ab initio molecular orbital theory and density functional theory calculations have been carried out on dimethoxymethane as a model for the anomeric effect. We optimized various conformations of dimethoxymethane using Gaussian 92 at the MP2/6-311 + + G**, MP2/DZP + Diffuse, MP2/6-31G**, and Becke3LYP/6-31G** levels of theory. These methods were evaluated based on their performance in reproducing structures and energies of dimethoxymethane when compared to experiment. This study also examined the structure and energy of dimethoxymethane as a function of dihedral angles for examining the anomeric effect at the MP2/6-31G** and Becke3LYP/6-31G** levels of theory. These calculations are qualitatively consistent with the anomeric effect observations in carbohydrates and with earlier calculations. Quantitative comparisons with earlier results reveal that dimethoxymethane has lower total energies, smaller rotational barriers, and shorter bond lengths than was previously determined. The Becke3LYP calculations were also compared to the MP2 results. The density functional theory findings show that the minimum energy structures correspond well with experimental and MP2 data. The total and relative energies from molecular orbital theory and density functional theory vary to some extent. Contour plots of the relative energies of dimethoxymethane were evaluated and compared to a relative energy contour plot determined by MM3. The contour plots were similar, showing slightly larger changes in energies for the MP2 results than for the Becke3LYP results, which in turn were slightly larger than the MM3 results. Density functional theory calculations are an excellent alternative method of calculation due to increased speed and reliable accuracy of the density functional calculations. These results will serve as a benchmark for modelling the anomeric effect in carbohydrates. © 1996 John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 767-780 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The molecular geometries of the 1-chloro-, 1-fluoro-, 1-methyl-, and 1-hydrogenosilatranes were fully optimized by the restricted Hartree-Fock (HF) method supplemented with 3-21G, 3-21G(d), 6-31G(d), and CEP-31G(d) basis sets; by MP2 calculations using 6-31G(d) and CEP-31G(d) basis sets; and by GGA-DFT calculations using 6-31G(d5) basis set with the aim of locating the positions of the local minima on the energy hypersurface. The HF/6-31G(d) calculations predict long (〉254 pm) and the MP2/CEP calculations predicted short (∼225 pm) equilibrium Si(SINGLE BOND)N distances. The present GGA-DFT calculations reproduce the available gas phase experimental Si(SINGLE BOND)N distances correctly. The solid phase experimental results predict that the Si(SINGLE BOND)N distance is shorter in 1-chlorosilatrane than in 1-fluorosilatrane. In this respect the HF results show a strong basis set dependence, the MP2/CEP results contradict the experiment, and the GGA-DFT results in electrolytic medium agree with the experiment. The latter calculations predict that 1-chlorosilatrane is more polarizable than 1-fluorosilatrane and also support a general Si(SINGLE BOND)N distance shortening trend for silatranes during the transition from gas phase to polar liquid or solid phase. The calculations predict that the ethoxy links of the silatrane skeleton are flexible. Consequently, it is difficult to measure experimentally the related bond lengths and bond and torsion angles. This is the probable origin of the surprisingly large differences for the experimental structural parameters. On the basis of experimental analogies, ab initio calculations, and density functional theory (DFT) calculations, a gas phase equilibrium (re) geometry is predicted for 1-chlorosilatrane. The semiempirical methods predict a so-called exo minimum (at above 310 pm Si(SINGLE BOND)N distance); however, the ab initio and GGA-DFT calculations suggest that this form is nonexistent. The GGA-DFT geometry optima were characterized by frequency analysis. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 835-840 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The structures of two isomers, difluorodisulfane (FSSF) and thiothionylfluoride(SSF2), and the corresponding transition structure were generated with density functional theory (DFT) methods. Three groups of DFT methods were used: local(Local Spin Density Approximation, LSDA), nonlocal (local with gradient corrections; BLYP and BP86), and hybrid methods that include a mixture of Hartree-Fock (HF) exchange with nonlocal correlation (Becke3BLYP, Becke3P86). An extended basis set [6-311 + + G(3df)] was used for all calculations, although satisfactory results can be obtained with the 6-311G(d) basis set. The geometries obtained were compared with both restricted Hartree-Fock (RHF) calculated and experimentally obtained values. The energy outcome and the activation barrier for the isomerization were evaluated. It was determined that excellent geometries can be obtained with the Becke3B86 hybrid method, whereas for reasonable energies MP2 single-point calculations on these geometries are necessary. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 851-863 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The concepts of symmetry-matrix and symmetry-supermatrix introduced in article I[J. Comput. Chem., 10, 957 (1989)] can be generalized to the Dirac-Fock method. By using the semidirect product decomposition of Oh and the linear vector space theory, the irreducible representation basis of Oh for any molecular system (Oh or its subgroups) can be deduced analytically in the nonorthonormal Cartesian Gaussian basis. This method is extended to discuss the double-valued representations of Oh* in the complex Cartesian Gaussian spinor basis. In the double-valued irreducible representation basis of D2*, the matrix of kinetic operator c(OVERLINE)σ(/OVERLINE)·(OVERLINE)p(/OVELINE) in the Dirac-Fock equation can be reduced into a real symmetric and can be grouped into classes under the operations in D3d. Therefore, the symmetry-matrix and symmetry-supermatrix can also be used in the Dirac-Fock method to reduce the storage of two electron integrals and calculations of Fock matrix during iterations by a factor of ca. g2 (g is the order of the molecular symmetry group). In addition, a method to deal with the nonorthonormal space is presented. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 888-904 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A comparison is made between geometry optimization in Cartesian coordinates, in Z-matrix coordinates, and in natural internal coordinates for the location of transition states. In contrast to the situation with minima, where all three coordinate systems are of comparable efficiency if a reliable estimate of the Hessian matrix is available at the starting geometry, results for 25 different transition states covering a wide range of structural types demonstrate that in practice Z-matrix coordinates are generally superior. For Cartesian coordinates, the commonly used Hessian update schemes are unable to guarantee preservation of the necessary transition state eigenvalue structure, while current algorithms for generating natural internal coordinates may have difficulty handling the distorted geometries associated with transition states. The widely used Eigenvector Following (EF) algorithm is shown to be extremely efficient for optimizing transition states. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 905-909 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Ab initio molecular orbital theory has been used to study the mechanism of the formation of C3H3+ from the reaction of CH3+ with acetylene. The highest level geometry optimizations and frequencies were computed at MP2-FC/6-31G**; single point energies of all the critical structures were computed to the MP4-FC/6-31G**//MP2-FC/6-31G** theory level. One of the three alternative transition structures leading to the formation of C3H3+ gives the cyclopropenyl cation and the other two the propargyl cation. The proportions of C3H2D+ and C3HD2+ obtained when CD3+ reacts with acetylene, and the composite nature of the metastable peak observed for the[C3H5]+→[C3H3]++ H2 fragmentation are explained by assuming a different degree of deuterium scrambling depending on the energy of the system. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 954-961 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The density or sum of states for a collection of independent oscillators, free rotors, and one-dimensional hindered rotors is obtained with good accuracy by numerical inversion of the corresponding total partition function by the method of steepest descents. The hindered-rotor partition functions are used in both classical and quantum forms, the latter in the approximation proposed by Truhlar [J. Comput. Chem., 12, 266 (1991)]. The numerical inversion compares well with analytical results obtained in a simple artificial case and also with an exact count of states in a large ethane-like system. Inversion of the hindered-rotor classical partition function is shown to lead to a somewhat different energy dependence of the sum or density of states, relative to the quantum counterpart, which is considered to be a more realistic representation. The routines presented are simple and fast enough to be of use in microcanonical rate calculations. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 1520-1531 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We report theoretical calculations of ion extraction selectivity by ionophores, based on molecular dynamics simulations coupled with the free energy perturbation technique. This method is applied to the Calix[4]-bis-crown6 (L) ionophore, which displays remarkable selectivity for Cs+ over Na+ extraction from an aqueous to a chloroform phase. Using a thermodynamic cycle, we model the cation extraction selectivity of L from water to chloroform and calculate a peak for Cs+, in agreement with the experiment. This high Cs+ ionophoricity is accounted for mostly by differential solvation effects, with standard 1-6-12 pairwise potentials without need of “special π interactions” with the ionophore. The effect of a picrate (Pic-) counterion on structures and selectivities is investigated. Finally, we report simulations on the L ionophore free and on the LCs+ and LCs+Pic- complexes at the water/chloroform interface. We find that all these species are “adsorbed” at the interface like surfactants instead of diffusing spontaneously to the organic phase. © 1996 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 17 (1996), S. 1559-1563 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Scattering matrices in an adiabatic basis were calculated for a model two-state atomic collision using a simple modification (normalization of the wave function) of the Fox - Goodwin three-point recurrence relation. Unlike the previous application of this method to scattering the present algorithm was able to precisely calculate the scattering matrix not only at low collision energies (eV), but also at high energies (keV). An analysis of the convergence of the modified Fox - Goodwin algorithm is also discussed for several angular momenta and for several energies where the results were compared to the renormalized Numerov method. © 1996 by John Wiley & Sons, Inc.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 727-758 
    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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    International Journal for Numerical Methods in Engineering 40 (1997), S. 777-796 
    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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    International Journal for Numerical Methods in Engineering 40 (1997), S. 2521-2577 
    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
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    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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    International Journal for Numerical Methods in Engineering 40 (1997), S. 2717-2737 
    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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    International Journal for Numerical Methods in Engineering 43 (1998), S. 507-532 
    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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    International Journal for Numerical Methods in Engineering 43 (1998), S. 941-953 
    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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    International Journal for Numerical Methods in Engineering 40 (1997), S. 551-563 
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; simultaneous optimization ; mixed convection ; finite element method ; material derivative concept ; adjoint variable method ; Engineering ; Numerical Methods and Modeling
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    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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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1437-1451 
    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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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1173-1191 
    ISSN: 0029-5981
    Keywords: warping ; bimoment ; Vlasov's thin-walled beam ; block stiffness matrix ; finite element method ; Engineering ; Numerical Methods and Modeling
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    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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    International Journal for Numerical Methods in Engineering 40 (1997), S. 3883-3900 
    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
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    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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    International Journal for Numerical Methods in Engineering 42 (1998), S. 1343-1390 
    ISSN: 0029-5981
    Keywords: optimal design ; design sensitivity ; direct differentiation method ; non-isothermal ; metal forming ; finite element method ; Engineering ; Numerical Methods and Modeling
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    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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    International Journal for Numerical Methods in Engineering 43 (1998), S. 33-50 
    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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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
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    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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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1859-1878 
    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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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2635-2646 
    ISSN: 0029-5981
    Keywords: non-linear elasticity ; finite element method ; Newton method ; Engineering ; Engineering General
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    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.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3123-3143 
    ISSN: 0029-5981
    Keywords: shotcrete ; finite element method ; viscoplasticity ; smeared cracking ; aging ; Rankine criterion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of the classical theory of viscoplasticity and its algorithmic formulation in the context of an operator split scheme is extended to account for the effect of aging. Within this framework, a 3-D multisurface constitutive model for shotcrete is proposed. A rotating-crack model based on the Rankine criterion is adopted in conjunction with a Drucker-Prager yield criterion for describing the mechanical behaviour of young concrete in the compressive regime. The model is suitable for the representation of the time-dependent behaviour of shotcrete including creep and the time dependence of strength and stiffness. A computationally effective return mapping scheme is achieved by formulating the material model in terms of the principal directions and transforming the obtained relations to global axes. Linearization of the return mapping algorithm yields the algorithmic tangent moduli.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3949-3968 
    ISSN: 0029-5981
    Keywords: finite element method ; crystal growth ; liquid phase electroepitaxy ; moving boundary ; Engineering ; Engineering General
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    Notes: A finite element numerical simulation model for the liquid phase electroepitaxial growth process of gallium arsenide is presented. The basic equations obtained from the fundamental principles of electrodynamics of continua, the constitutive equations for the liquid and solid phases derived from a rational thermodynamic theory, and the associated interface and boundary conditions are presented for a two-dimensional axisymmetric growth cell configuration.The field equations are solved numerically by an adaptive finite element procedure. The effect of moving interfaces is taken into account. Numerical simulations are carried out for different convection levels by changing the value of the gravitational constant. Results show that convection has significant effect on the growth process under normal gravity conditions and results in thickness non-uniformity of the grown layers. The thickness non-uniformity leads to curved interfaces of growth and dissolution, which enhance convection.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3529-3544 
    ISSN: 0029-5981
    Keywords: multilevel iterative method ; finite element method ; structural analysis ; aggregation method ; preconditioner ; equation solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present study is aimed to overcome difficulties faced with industrial applications of multilevel iterative methods to arbitrary finite element (FE) structural analysis problems. The coarse grid concept, used in multigrid methods, is substituted with an aggregation coarse model based on the mechanical principle. On the base of this approach together with previously developed multilevel preconditioner, an efficient iterative equation solver FEAGS was developed for using in standard comprehensive finite element software systems. Numerical examples for analyses of three-dimensional (3-D) frame structures demonstrate the efficiency of the method. Comparison with incomplete Cholesky conjugate gradient (ICCG) method and direct methods is presented.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2647-2671 
    ISSN: 0029-5981
    Keywords: hierarchic models ; laminated composites ; stress-based formulation ; complementary energy ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubeke's dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2575-2591 
    ISSN: 0029-5981
    Keywords: finite element method ; numerical analysis ; numerical method ; groundwater modelling ; subsurface modelling ; groundwater pollution modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Real world ground water pollution modelling deals with solute transport through anisotropic, heterogeneous media. The applicability of analytical solutions for such a real world system is extremely limited. As an effective tool, numerical models, such as finite difference and finite element methods, are usually employed to model field scenarios. Nevertheless, ground water pollution modelling is a hallenging task and frequently ends up with misleading results. Most of the time insufficient data are blamed for such erratic results. A recent investigation shows that the shortcomings of numerical formulations may be the major cause for many disputes and confusions in numerical analyses. In reality, a point injection of water in a static, homogeneous and isotropic groundwater system shows a radial dissipation of water forming a sphere; and a full-depth line injection shows a radial dissipation forming a cylinder. The finite difference method completely ignores this fundamental flow principles and allows water only to flow along orthogonal directions. To overcome this limitation, the finite element method was developed as a flexible approach in order to connect a node with the neighbouring nodes in various directions where water is assumed to flow in any directions along node connections. In a recent investigation, it has been found that the conventional finite element method does not keep the commitments; and its formulation techniques lead to a global matrix where a solution domain is not connected with all the neighbouring nodes and does not comply with the control-volume mass balance concept. A consistent finite element formulation approach which does not need imaginary mathematical formulation and overcomes the limitations of both the conventional finite difference and finite element methods has been developed. This method allows fluid flow and solute transport in a porous medium in radial directions. The global matrices for flow and transport obtained from this technique are field representative, diagonally dominant and easily convergent. The new method is robust, needs less mathematical computation and has many advantages over the conventional finite difference and finite element methods.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3391-3403 
    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3145-3162 
    ISSN: 0029-5981
    Keywords: shotcrete ; tunnelling ; cap model ; New Austrian Tunnelling Method (NATM) ; finite element method ; viscoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the parameter identification, verification and selected applications of a 3D viscoplastic material model for shotcrete proposed by Meschke. The performance of the shotcrete model is evaluated by means of reanalyses of short-term and creep tests on shotcrete specimen. The most essential items of a viscoplastic cap model used for the representation of soil including the determination of the model parameters are also presented. Both models are employed in a 3D finite element simulation of the excavation of a single-track tunnel driven according to the New Austrian Tunnelling Method. Comparisons between in situ measurements and numerical results are presented.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3065-3082 
    ISSN: 0029-5981
    Keywords: biomechanics ; damage ; finite element method ; plasticity ; standard generalized material ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Motivated by mechanical analysis of cancellous bone, a 3D constitutive law describing the simultaneous flow of rate-independent plasticity and damage is developed in the framework of thermodynamics of irreversible processes with internal variables. Following the hypothesis of standard generalized materials, a free energy and a dissipation potential are postulated and the associated flow rules derived with the tools of convex analysis. On the computational side, the classical implicit projection (or catching up) algorithm used in plasticity is extended to account for the additional flow of damage. Due to the existence of a dissipation potential, linearization of the incremental algorithm provides a symmetric tangent operator. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the quadratic convergence of the algorithm.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 51-65 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1171-1200 
    ISSN: 0029-5981
    Keywords: hyperelasticity ; stability problems ; finite element method ; spectral decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a finite element method is developed to treat stability problems in finite elasticity. For this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches. These results can then be used to derive an efficient numerical scheme for the computation of singular points.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 4363-4404 
    ISSN: 0029-5981
    Keywords: large strains ; stress update ; error analysis ; convected frames ; nonlinear computational mechanics ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 453-471 
    ISSN: 0029-5981
    Keywords: multi-level method ; aggregation method ; large scale problems ; finite element method ; structural dynamics ; generalized eigen value problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a novel iterative method of multilevel type for solving large-scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modification of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low-frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems. Numerical experiments performed for three-dimensional truss, frame and solid structures demonstrate an excellent performance of the method. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 511-531 
    ISSN: 0029-5981
    Keywords: dynamic contact ; multibody dynamics ; kinematic constraint ; vehicle ; flexible structure ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the dynamic analysis of vehicles moving on flexible structures which contain gaps. The Lagrange multipliers associated with the kinematic constraints of the vehicle components and the contact forces between the rigid wheels of the vehicle and the flexible structures are simultaneously computed with the solutions of the equations of motion by using the iterative schemes. On the kinematic joints and on the possible contact points the velocity and acceleration constraints as well as the displacement constraints are satisfied by the monotone reductions of the corresponding error vectors. And a well-developed simple one-step time integration of ordinary differential equation is employed for the solution of the equations of motion. Convergences of the iterative schemes are analysed and numerical simulations are conducted. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1901-1916 
    ISSN: 0029-5981
    Keywords: plasticity ; friction ; torsion ; finite element method ; equilibrium model of FEM ; variational inequalities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The quasi-static problem of torsion of an elastic-plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic-plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law - it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 2055-2082 
    ISSN: 0029-5981
    Keywords: finite element method ; Steklov method ; singular points ; failure/fracture analysis ; eigenpairs ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points. The singularities may be caused by re-entrant corners and abrupt changes in boundary conditions or material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes.This paper addresses the problem of determining the eigenpairs numerically on the basis of the Steklov formulation. Numerical results are presented for several cases. Importantly, the method is applicable to three-dimensional cases.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1413-1433 
    ISSN: 0029-5981
    Keywords: finite element method ; adaptive refinement ; shape sensitivity analysis ; error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the Zienkiewicz-Zhu estimator was extended to the estimation of the discretization error arising from shape sensitivity analysis using the finite element method. The sensitivity error was quantified from the sensitivity of the energy norm by using an estimator specially developed for this purpose. Sensitivity analyses were carried out using the discrete analytical approach, which introduced no additional errors other than the discretization error. In this work, direct nodal averaging was used for linear triangular elements and the SPR technique for quadratic elements in order to obtain the smoothed stress and sensitivities fields. Two examples with an exact solution are used to analyse the effectivity of the proposed estimator and its convergence with the h-adaptive refinement. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 561-578 
    ISSN: 0029-5981
    Keywords: finite element method ; adaptivity ; a posteriori error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector field computed from the finite element solution. This estimator, designed for p- and hp-extensions, is conceptually different from estimators based on residuals or patch recovery which are designed for h-extension procedures. The quality of the error estimator is demonstrated by examples. The results show that the effectivity index is reasonably close to unity and the sequences of p-distributions obtained with the error indicators closely follow the optimal trajectory. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 4477-4499 
    ISSN: 0029-5981
    Keywords: shell element ; higher-order theory ; facet composite shell element ; flat shell element ; finite element method ; shear deformable flat shell element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A C0 finite element formulation of flat faceted element based on a higher-order displacement model is presented for the analysis of general, thin-to-thick, fibre reinforced composite laminated plates and shells. This theory incorporates a realistic non-linear variation of displacements through the shell thickness, and eliminates the use of shear correction coefficients. The discrete element chosen is a nine-noded quadrilateral with five and nine degrees of freedom per node.A comparison of results is also made with the 2-D thin classical and 3-D exact analytical results, and finite element solutions with 9-noded first-order element. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 443-472 
    ISSN: 0029-5981
    Keywords: finite element method ; error estimation ; stress recovery ; Engineering ; Numerical Methods and Modeling
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    Notes: In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress field. The qualitative properties of the recovered stress field necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A specific procedure for recovery of an improved stress field is then developed. The procedure can be classified as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisfied a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 685-702 
    ISSN: 0029-5981
    Keywords: asymptotic postbuckling ; stability ; finite element method ; smooth stresses ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution, the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick convergence of the postbuckling coefficients. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4159-4182 
    ISSN: 0029-5981
    Keywords: shallow water equations ; finite element method ; Lagrangian framework ; fluid particle trajectories ; Tay estuary ; Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: In this paper we describe a new finite element model for the tidal hydrodynamics in estuaries. The mathematical model is based on the solution of the two-dimensional shallow water equations in a Lagrangian framework which is defined along the trajectories of fluid particles. This method gives a flexible and robust numerical scheme for moving boundary flows encountered in tidal water systems. In order to validate the developed model we have, at first instance, compared our numerical results with analytical solutions obtained for domains with simple geometries. Further tests are then conducted to demonstrate the model's ability to cope with conditions such as hydraulic shock, abrupt changes in the flow domain geometry and gradual changes of water surface breadth. The change in the water surface breadth corresponds to the drying and wetting of the plains along the banks of a typical tidal river/estuary reach. The drying and wetting of flood plains result in the existence of very shallow depth of water at some sections of the flow domain during a tidal cycle. The flow equations under these conditions are strongly convection dominated. Previously published tidal models rely on either, some form of upwinding or the use of extremely fine meshes to give stable results for the convection dominated very shallow depth computations in estuaries. We show that our model can yield stable and accurate results for very shallow depths in the tidal flow domains without using any kind of artifical damping or excessive mesh refinement. Computational costs of simulating hydrodynamical conditions in a natural water course, even using a depth averaged two-dimensional approach, can be very high. The ability of our scheme to cope with convection dominated conditions has enabled us to economize the computational efforts by using coarse meshes in our finite element calculations. After the validation stage, the developed model is applied to simulate the tidal conditions in a real estuary. The comparison of the model results with the field observations shows a close agreement between these sets of data
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 407-421 
    ISSN: 0029-5981
    Keywords: finite element method ; enhanced strain method ; symbolic integration ; Engineering ; Numerical Methods and Modeling
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    Notes: A class of enhanced strain four-node elements with Taylor expansion of the shape function derivatives is presented. A new concept of enhancement using besides the ‘standard’ enhanced strain fields also two other enhanced fields is developed on the basis of the Hu-Washizu principle. For first-order Taylor expansion enhanced modes become uncoupled, thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed. Furthermore, the formulation permits a symbolic integration, which leads to a closed-form solution for the element tangent matrix. Several numerical examples show that the element is stable, invariant, passes the patch test and yields good results especially in the highly distorted regime. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 905-917 
    ISSN: 0029-5981
    Keywords: linear elastic fracture mechanics ; finite element method ; stress intensity factor ; energy release rate ; three-dimensional crack growth ; composite materials ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical procedure to model the crack front evolution of initially arbitrary shaped planar cracks in a three-dimensional solid. The influence of a bimaterial interface on the fracture path of a semi-elliptical surface crack in a three-dimensional structure is examined. The analysis is based on the assumption that fracture is controlled by small-scale yielding and linear elastic fracture mechanics. The finite element method and the crack-tip contour J-integral in a volume domain representation are utilized to calculate the crack front energy release rate. The computed values of the energy release rate are used with a crack-tip velocity growth law to model crack growth increment. The progress of the crack growth evolution is brought forward by successive iterations. Examples of computed crack evolution are given for an embedded circular crack, a semi-elliptical surface crack in a finite plate, and a configuration that defines an isotropic homogeneous material layer with a surface crack located between two material layers. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1525-1550 
    ISSN: 0029-5981
    Keywords: adjoint problem ; discrete curvature ; finite element method ; free surface flow ; optimization ; quasi-Newton method ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 739-757 
    ISSN: 0029-5981
    Keywords: finite element method ; crack propagation ; low cycle fatigue ; remeshing ; Engineering ; Numerical Methods and Modeling
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    Notes: An algorithm is presented which allows for fully automatic linear elastic low cycle fatigue (LCF) crack propagation calculations of mode I plane cracks in large structures by means of the finite element technique. The bulk of the algorithm consists of an automatic procedure to introduce the geometry of a plane crack with an arbitrary crack front in an existing three-dimensional (3-D) mesh. Once the K-distribution for the initial crack has been calculated, the use of the superelement technique reduces the computing time for the subsequent cycles by a factor of up to 40 or more. Two industrial examples illustrate the accuracy and effectiveness of the method. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 2267-2288 
    ISSN: 0029-5981
    Keywords: finite element method ; viscoelasticity ; incremental constitutive law ; Engineering ; Numerical Methods and Modeling
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    Notes: This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the finite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the finite element solution. Use is made of a Dirichlet-Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 3279-3295 
    ISSN: 0029-5981
    Keywords: block solver ; unsymmetric matrix ; sparse ; banded ; linear equations ; finite element method ; Engineering ; Numerical Methods and Modeling
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    Notes: A block equation solver for the solution of large, sparse, banded unsymmetric system of linear equations is presented in this paper. The method employs Crout variation of Gauss elimination technique for the solution. The solver ensures the efficient use of the available memory by doing block factorization and storage. It uses a skyline storage scheme which will avoid unnecessary operations on zero elements above the skyline which has found widespread use in banded symmetric solvers. A FORTRAN code with ample comments is provided. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 3443-3462 
    ISSN: 0029-5981
    Keywords: finite element method ; Helmholtz equation ; a posteriori error estimation ; acoustic scattering ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: This paper contains a first systematic analysis of a posteriori estimation for finite element solutions of the Helmholtz equation. In this first part, it is shown that the standard a posteriori estimates, based only on local computations, severely underestimate the exact error for the classes of wave numbers and the types of meshes employed in engineering analysis. This underestimation can be explained by observing that the standard error estimators cannot detect one component of the error, the pollution error, which is very significant at high wave numbers. Here, a rigorous analysis is carried out on a one-dimensional model problem. The analytical results for the residual estimator are illustrated and further investigated by numerical evaluation both for a residual estimator and for the ZZ-estimator based on smoothening. In the second part, reliable a posteriori estimators of the pollution error will be constructed. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 4259-4271 
    ISSN: 0029-5981
    Keywords: finite element method ; mass matrix ; Engineering ; Numerical Methods and Modeling
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    Notes: A new approach to constructing mass matrices is presented, based on expressing it through use of a variable parameter. This allows the mass matrix to be adjusted in such a way that a simple eigenvalue problem get the best solution possible in terms of some error measure. This procedure is used to create both diagonal mass matrices and mixed mass matrices. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 219-236 
    ISSN: 0029-5981
    Keywords: secant and tangent stiffness matrices ; structural analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
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    Notes: The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non-linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 885-901 
    ISSN: 0029-5981
    Keywords: ground temperature ; golf links ; pesticide pollution ; finite element method ; optimal control ; bang-bang control ; practical use ; Engineering ; Engineering General
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    Notes: The calculation and physical experiment related to control of the ground temperature by bang-bang control theory are discussed in this paper. Comparing the computed results with the results obtained by the experiments and measurements, it is shown that the bang-bang control theory is adaptable for practical use. The basic equation of the ground temperature is discretized by the finite element method in space and the Crank-Nicolson method in time. To obtain the optimal control temperature, the performance function is minimized by the Sakawa-Shindo method.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 601-629 
    ISSN: 0029-5981
    Keywords: finite element method ; scattering problems ; open boundaries ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: An iterative procedure is described for the finite-element solution of scalar scattering problems in unbounded domains. The scattering objects may have multiple connectivity, may be of different materials or with different boundary conditions. A fictitious boundary enclosing all the objects involved is introduced. An appropriate Robin (mixed) condition is initially guessed on this boundary and is iteratively improved making use of Green's formula. It will be seen that the best choice for the Robin boundary condition is an absorbing-like one. A theorem about the theoretical convergence of the procedure is demonstrated. An analytical study of the special case of a circular cylindrical scatterer is made. Comparisons are made with other methods. Some numerical examples are provided in order to illustrate and validate the procedure and to show its applicability whatever the frequency of the incident wave. Although particular emphasis is laid in the paper on electromagnetic problems, the procedure is fully applicable to other kinds of physical phenomena such as acoustic ones. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 749-772 
    ISSN: 0029-5981
    Keywords: crack ; propagation ; remeshing ; mode-I ; three-dimensional ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A previous article (G. Dhondt, ‘Automatic 3-D mode I crack propagation calculations with finite elements’, Int. J. Numer. Meth. Engng. 41, 739-757 (1998)) has illustrated how automatic 3-D mode I cyclic crack propagation calculations making repeated use of the finite element method can be performed for structures in which the crack plane is made up of element faces. In the present paper an automatic cutting procedure is proposed which allows the method to be applied to arbitrarily meshed structures for which the crack plane intersects the elements. New 20-node brick elements are automatically generated and a subsequent smoothing procedure improves the quality of the resulting mesh. The method is illustrated by cyclic crack propagation calculations in a specimen and an industrial component. © 1998 John wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 269-294 
    ISSN: 0029-5981
    Keywords: centrifugal pumps ; potential fluid flow ; unsteady flow ; fluid forces ; finite element method ; perturbation analysis ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics , Technology
    Notes: A finite element based method has been developed for computing time-averaged fluid-induced radial excitation forces and rotor dynamic forces on a two-dimensional centrifugal impeller rotating and whirling in a volute casing. In this method potential flow theory is used, which implies the assumption of irrotational inviscid flow. In comparison with other analyses of fluid-induced impeller forces, two main features have been included. Firstly, the hydrodynamic interaction between impeller and volute isproperly modelled. Secondly, the variation of the width of the volute has been adequately included in the two-dimensional analysis by a modification of the equation of continuity. A regular perturbation method is used to deal with the effects of the whirling motion of the impeller. The excitation forces are calculated from the zeroth-order problem in which the impeller axis is placed at the volute origin. The rotor dynamic forces associated with the whirling motion of the impeller are derived from the first-order solution. The force components, tangential and normal to the whirl orbit, are predicted as functions of the impeller--volute geometry, the flow conditions and the whirl speed ratio. The method is applied to a centrifugal pump experimentally tested at the California Institute of Technology. Comparisons between predictions and experimental data show the capabilities of the proposed method to reproduce the main features of fluid-induced impeller forces in centrifugal pumps. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1053-1068 
    ISSN: 0029-5981
    Keywords: finite element method ; variational inequalities ; contact problems ; heuristic algorithms ; nondifferential optimization methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article is devoted to the development of a new heuristic algorithm for the solution of the general variational inequality arising in frictional contact problems. The existing algorithms devised for the treatment of the variational inequality representing frictional contact rely on the decomposition of the physical problem into two sub-problems which are then solved iteratively. In addition, the penalty function method and/or the regularization techniques are typically used in the solution of these reduced sub-problems. These techniques introduce user-defined parameters which could influence the convergence and accuracy of the solution. The new method presented in this article overcomes these difficulties by providing a solution for the general variational inequality without decomposition into sub-problems. This is accomplished using a new heuristic algorithm which utilizes mathematical programming techniques, and thus avoids the use of penalty or regularization methods. The versatility and reliability of the developed algorithm were demonstrated through implementation to the case of frictional contact of an elastic hollow cylinder with a rigid foundation. © 1998 John Wiley & Sons, Ltd.
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