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  • 101
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 197-208 
    ISSN: 1069-8299
    Keywords: curved surface ; triangular mesh ; automatic generation ; Bézier patches ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the discretization of any given multi-connected curved surface into triangular elements with straight sides. The method evolves from an initial rough triangular mesh generated from a set of input points which describe the geometry of the problem domain. Interior nodes are distributed according to user-established node-spacing functions of pre-specified spacing control parameters, and they are linked using the advancing front technique. Particular attention is paid to obtaining good distribution of interior nodes in the vicinity of the domain limits. Surface geometry representation is established using triangular Bézier patches with G1 continuity. This approach ensures a geometrically well-defined working platform for the subsequent discretization of the problem domain. The proposed method requires minimum input from the user and allows mesh gradation and remeshing to be carried out in a straightforward manner. Furthermore, problems associated with variations in the domain geometry as a result of local remeshing are eliminated with the aid of the geometrically pre-defined discretization platform. Results are presented for a range of both curved and planar surfaces, typical of those which might be encountered in hydrodynamics modelling involving flows with a free surface. The presented results demonstrate the flexibility and power of the technique.
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  • 102
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    Communications in Numerical Methods in Engineering 12 (1996), S. 229-234 
    ISSN: 1069-8299
    Keywords: higher-order beam element ; best-fit stress prediction ; a priori error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is known that finite elements try to capture stresses within each discretized local region in a ‘best-fit’ sense. In the paper we examine the performance of a beam element based on a higher-order shear deformation theory and show that the best-fit paradigm accounts for the manner in which through-the-thickness displacement and stresses are modelled. An a priori prediction derived from the paradigm is confirmed by a carefully chosen numerical experiment. This provides a measure of the quality of approximation as well as another ‘falsification’ of the best-fit paradigm.
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  • 103
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    Communications in Numerical Methods in Engineering 12 (1996), S. 223-228 
    ISSN: 1069-8299
    Keywords: Discretization ; heat conduction ; simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A different approach to discretization is described with which complicated three-dimensional heat transfer problems can be solved with a finite volume approach on a general curvilinear grid. It represents an improvement on the existing methods in that it can easily be expanded to three-dimensional problems. A concise explanation of the transformation process is given, together with a discussion of the discretization procedure. The method is evaluated by solving two simple test problems and comparing the results with those of existing methods and the analytical solution. In conclusion it is found that this method yields equally or more accurate results than the existing methods, with the additional advantage of being easily expandable to three-dimensional problems.
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  • 104
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    Communications in Numerical Methods in Engineering 12 (1996), S. 243-248 
    ISSN: 1069-8299
    Keywords: finite elements ; automatic generation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element generation methods, such as Delaunay, allow the meshing of shapes from a set of nodes. These nodes must previously exist. The authors present a simple, fast and reliable method to generate them in an unstructured way in N-dimensional space. Its main characteristic is to easily allow variation of the node density by introducing a density function, either analytical or discretized. This function can also be anisotropic. Some nodes can have a pre-fixed position. Inner lines and holes can also be specified in the domain to be meshed. Generated nodes are to be connected according to triangles in 2D and tetrahedrals in 3D.
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  • 105
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    Communications in Numerical Methods in Engineering 12 (1996), S. 235-242 
    ISSN: 1069-8299
    Keywords: finite member element ; modified theory ; geometrical non-linearity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a modified non-linear member element is derived which can lead to satisfactory computed results even for large loading and displacement increments from pre-instability to post-instability of structures. The high accuracy of this element is proved by numerical examples.
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  • 106
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 107
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    Communications in Numerical Methods in Engineering 12 (1996), S. 249-256 
    ISSN: 1069-8299
    Keywords: obstacle problems ; quadratic programming ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of problems involving frictionless contact between an elastic body and a rigid obstacle is considered. The elastic body may undergo small or large deformation. Finite element discretization and repetitive linearization lead to a sequence of quadratic programming (QP) problems for incremental displacement. The performances of several QP algorithms, including two new versions of a modified steepest descent algorithm, are compared in this context. Numerical examples include a string, a membrane and an Euler-Bernoulli beam, in contact with flat and non-flat rigid obstacles.
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  • 108
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    Communications in Numerical Methods in Engineering 12 (1996), S. 317-319 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 109
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    Communications in Numerical Methods in Engineering 12 (1996), S. 271-280 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors study the shape optimization of a complex cracked shell under complex criteria. The shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turboshaft. The optimization criteria involved are of course the weight of the structure, but also the plastic instability and critical stress intensity factor. All computations have been made with the Ansys finite element program in which an optimization module exists.
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  • 110
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    Communications in Numerical Methods in Engineering 12 (1996), S. 257-267 
    ISSN: 1069-8299
    Keywords: mode-matching ; Helmholtz' equation ; DtN ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.
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  • 111
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    Communications in Numerical Methods in Engineering 12 (1996), S. 281-294 
    ISSN: 1069-8299
    Keywords: wavelets ; measures ; stability ; domains ; differential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation.
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  • 112
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    Communications in Numerical Methods in Engineering 12 (1996), S. 371-372 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 113
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    Communications in Numerical Methods in Engineering 12 (1996), S. 295-302 
    ISSN: 1069-8299
    Keywords: mesh generation ; adaptivity ; iterated fractal systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one.
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  • 114
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    Communications in Numerical Methods in Engineering 12 (1996), S. 303-316 
    ISSN: 1069-8299
    Keywords: stretching functions ; mesh refinement ; finite differences ; truncation error ; composite grids ; regularity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work the truncation-error criteria of Thompson and Mastin (1985) are combined with conditions of vanishing second and higher derivatives at both endpoints for the purpose of deriving new classes of one-dimensional stretching functions for mesh refinement in finite-difference numerics. With these elementary stretching functions, matching of the slopes between adjacent grid patches then automatically confers Cn regularity upon the composite stretching function. Formulated with reference to two conceptions of truncation order (fixed relative distribution against fixed number of nodes) the resulting mappings are shown to provide particularly advantageous node distributions at both ends simultaneously (with concomitantly higher truncation error in between). Viewed overall, the truncation-error functions compare favourably with those for sinh, tanh and erf - mappings whose utility for mesh refinement was established by Thompson and Mastin. The numerical labour of implementing the new stretching functions is only slightly greater than that required for the error function. An illustrative derivation involving Cn patching leads to two-sided stretching functions, which allow the slopes at both ends to be prescribed arbitrarily. This formulation differs from a previous approach described by Vinokur (1983).
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  • 115
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    Communications in Numerical Methods in Engineering 12 (1996), S. 331-341 
    ISSN: 1069-8299
    Keywords: glass ; finite element ; strategy's creep forming ; sheet ; manufacture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An original optimization strategy for creep forming is carried out by finite element thermodependent viscoplastic models. For reference design glass products, an optimum forming database is developed in two steps: the first step analyses feasibility, with elastic and viscoplastic finite element models, with regard to initial manufacture choices. With thermodependent viscoplastic finite element models, the second step leads to optimum forming parameters, concerning skeleton bending radii and/or non-homogeneous heating adjustments.
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  • 116
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    Communications in Numerical Methods in Engineering 12 (1996), S. 321-330 
    ISSN: 1069-8299
    Keywords: solid-shell structure ; 3D solid element ; degenerated shell element ; DOF expanding ; multipoint constraint equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a degree of freedom expanding method for dealing with the connections of 3D isoparametric solid elements and the degenerated shell elements. By introducing two degrees of freedom to describe the elongation in the normal direction of the shell node linked with solid elements, a series of multipoint constraint equations which provide proper connections of solid and shell nodes are raised. The method gives a complete solution to the problem of connection between 3D isoparametric solid elements and degenerated shell elements even for the thermal elasto-plastic problem. It can adapt to complex junctions and simplify programming. Numerical examples are also presented to demonstrate the accuracy and feasibility in thermal elasto-plastic analysis.
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  • 117
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    Communications in Numerical Methods in Engineering 12 (1996), S. 351-357 
    ISSN: 1069-8299
    Keywords: anisotropy ; finite elements ; layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification of the usual quadrangle (2D) and brick (3D) finite element for field problems is proposed. It allows the principal directions of the conductivity tensor (anisotropy directions) to be derived from the geometrical shape of the finite element and to change within it. An internal layering is assumed which is parallel to the boundary at two opposite faces (top and bottom) of the element. Without an explicit computation of angles the anisotropy directions are parallel and perpendicular to this layering. An application is the modelling of pore fluid flow in sedimentary basins.
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  • 118
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    Communications in Numerical Methods in Engineering 12 (1996), S. 343-349 
    ISSN: 1069-8299
    Keywords: mesh generation ; Delaunay mesh ; Watsens method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Automated mesh generation using a combined octree/Delaunay approach typically requires that rectangular elements be bounded by other rectangular elements which are not more that one division smaller (i.e. 1/8 the volume in 3D). This limitation is sometimes referred to as the 2 : 1 rule. This paper presents a modification which allows for any level of difference.
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  • 119
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
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  • 120
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    Communications in Numerical Methods in Engineering 12 (1996), S. 359-369 
    ISSN: 1069-8299
    Keywords: Navier-Stokes ; artificial compressibility methodology ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the problem of laminar incompressible viscous flow through a wavy channel. An artificial compressibility method using the approximate factorization technique is applied to solve the velocity-pressure formulation of the Navier-Stokes equations written in curvilinear non-orthogonal coordinates. The physical domain used was one wavelength of the channel in which appropriate periodicity conditions were applied in order to find a solution independent of entry effects. Flow separation was observed for high Re numbers and/or large wave amplitudes of the channel. The effect of inertia to the velocity profiles was observed, and pressure and shear stress were calculated along the length of the channel. These flows have great interest in industry and medicine such as for the extracorporeal membrane oxygenator.
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  • 121
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    Communications in Numerical Methods in Engineering 12 (1996), S. 445-446 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 122
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    Communications in Numerical Methods in Engineering 12 (1996), S. 383-394 
    ISSN: 1069-8299
    Keywords: symmetrically laminated plates ; anisotropy ; fundamental solutions ; boundary integral equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the bending problem of moderately thick symmetrically laminated anisotropic plates is considered, based on the first-order transverse shear deformation plate theory. Using the method of plane wave decomposition and Hörmander's operator method, the fundamental solution of the plates is presented. The boundary integral equation of the plates is formulated by taking the fundamental solution presented as the weighted function and using the method of weighted residuals. The numerical calculation of the boundary integral equation presented is discussed in detail. Some examples are presented and compared with the exact solutions and the numerical solutions available in the literature. The numerical results show that the present method has a satisfactory rate of convergence and acceptable accuracy with a reasonable boundary mesh.
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  • 123
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    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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  • 124
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    Communications in Numerical Methods in Engineering 12 (1996), S. 395-411 
    ISSN: 1069-8299
    Keywords: finite volume ; high-order discretization ; non-oscillatory schemes ; pressure interpolation ; non-staggered grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the problem of convection discretization by extension and application of numerical schemes used in compressible flows: SONIC-A, SONIC-B, UNO2, MUSCL and MINMOD to predict steady incompressible recirculating convection dominated flows. A new scheme, SONIC-Q, is proposed together with a third-order non-oscillatory practice for pressure interpolation in non-staggered grids. Finite-volume calculations of the Navier-Stokes equations of a standard 2D driven square cavity standard test case and the laminar flow over a fence using primitive variables and non-staggered grid systems have shown that the schemes are alternatives to the conventional ones used in general algorithms for incompressible recirculating flows. In general these composite high-order schemes have proved to be good candidates to overcome the problems of false-diffusion and unboundedness encountered in non-composite high-order upwind schemes used in incompressible flows.
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  • 125
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    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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  • 126
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    Communications in Numerical Methods in Engineering 12 (1996), S. 413-424 
    ISSN: 1069-8299
    Keywords: boundary integral equation ; necessary and sufficient condition ; plane elasticity problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With respect to a given boundary value problem, the corresponding conventional boundary integral equation is shown to yield non-equivalent solutions, which are dependent upon Poisson's ratio and geometry. In the paper a systematic method for establishing a necessary and sufficient boundary integral formulation has been proposed for two-dimensional elastostatic problems. Numerical analyses show that the conventional boundary integral equation yields incorrect results when the scale in the fundamental solution approaches a degenerate scale value. However, the results of the necessary and sufficient boundary integral equation are in good agreement with analytical solutions of the boundary value problem.
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  • 127
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    Communications in Numerical Methods in Engineering 12 (1996), S. 519-520 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
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  • 128
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Keywords: Engineering ; Engineering General
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  • 129
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    Communications in Numerical Methods in Engineering 12 (1996), S. 433-444 
    ISSN: 1069-8299
    Keywords: two-phase flow ; solute transport ; interphase exchange ; porous media ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a numerical method for modelling two-phase flows and solute transport, particularly with interphase exchange in porous media, is presented. The governing equations are derived to describe two immiscible and compressible fluids flows such as water-air and two-phase solute transport with interphase exchange. Technically, the standard finite element method and a strongly implicit procedure are employed to solve the fully coupled governing equations. Pressures of two-phase fluids and solute concentrations in two-phase fluids are taken as the primary unknown variables, and the discretized equations are solved by a direct type of solver. Application examples are shown to confirm the applicability of the numerical method.
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  • 130
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    Communications in Numerical Methods in Engineering 12 (1996), S. 447-454 
    ISSN: 1069-8299
    Keywords: inviscid drops ; coalescence ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is used to simulate the motion of inviscid drops colliding and coalescing at a solid surface. The equations of motion are solved by a boundary element method in which the free surface of the drop is represented by a moving grid. The numerical results include the configuration of the drop during coalescence and the kinetic and potential energies. A numerical example is used to demonstrate the way in which coalescence affects the configuration of the free surface.
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  • 131
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    Communications in Numerical Methods in Engineering 12 (1996), S. 455-459 
    ISSN: 1069-8299
    Keywords: harmonic differential quadrature method ; computational complexity ; differential quadrature ; numerical method ; centrosymmetric matrix ; computational mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of weighting coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
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  • 132
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    Communications in Numerical Methods in Engineering 12 (1996), S. 471-482 
    ISSN: 1069-8299
    Keywords: numerical methods ; constitutive equations ; composite ; mixing formulation ; anisotropic elastoplastic model ; mapping stress tensor space ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo-elasto-plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
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  • 133
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    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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    Communications in Numerical Methods in Engineering 12 (1996), S. 461-470 
    ISSN: 1069-8299
    Keywords: linear polyhedra ; symbolic integration ; polynomial functions ; monomials ; tetrahedron ; hexahedron ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper concerns analytical integration of polynomial functions over linear polyhedra in three-dimensional space. To the authors' knowledge this is a first presentation of the analytical integration of monomials over a tetrahedral solid in 3D space. A linear polyhedron can be obtained by decomposing it into a set of solid tetrahedrons, but the division of a linear polyhedral solid in 3D space into tetrahedra sometimes presents difficulties of visualization and could easily lead to errors in nodal numbering, etc We have taken this into account and also the linearity property of integration to derive a symbolic integration formula for linear hexahedra in 3D space. We have also used yet another fact that a hexahedron could be built up in two, and only two, distinct ways from five tetrahedral shaped elements These symbolic integration formulas are then followed by an illustrative numerical example for a rectangular prism element, which clearly verifies the formulas derived for the tetrahedron and hexahedron elements.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 497-505 
    ISSN: 1069-8299
    Keywords: weight function approach ; edge crack problem ; Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: A fundamental field for the edge crack problem is suggested, and the field is composed of the singular displacement field and the complementary regular field. The boundary displacement of the fundamental field plays the role of the weight function in the edge crack problem. After multiplying the boundary traction in the physical problem with the weight function and performing integration along the boundary, the stress intensity factor at the crack tip is obtainable. Numerical examples are given to demonstrate the use of the suggested weight function approach.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 543-555 
    ISSN: 1069-8299
    Keywords: control volume method ; finite element interpolation ; fluid flow ; upwind schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Together with the finite element method (FEM), the control volume method (CVM) is of particular interest for the numerical solution of partial differential equations. The accuracy of computation of the CVM almost matches that of FEM in contour-adapted co-ordinates or block-structured meshes of a single element type. The CVM is superior to the FEM in terms of physical interpretation and ease of handling. The paper presents an interpretation of the FEM that allows it to be treated like a CVM. This formal CVM, which is based on FEM techniques, combines the advantages of both methods. The method is applied to the discretization of the Navier-Stokes equation.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 557-568 
    ISSN: 1069-8299
    Keywords: hyperbolic equations ; finite-difference methods ; Padé approximants ; sequential and parallel implementation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 507-517 
    ISSN: 1069-8299
    Keywords: non-linear constitutive model ; anisotropy ; finite strains ; axisymmetrical finite elements ; vascular biomechanics ; soft tissue biomechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To explore the mechanical non-linear behaviour of anisotropic arterial walls on a computational basis, the formulation of a continuum based elastic potential is a major task and challenge to the analyst. The present communication is concerned with the constitutive modelling and numerical analysis of vascular segments covering finite strains. Special attention is paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain. Axisymmetrical membrane elements are assembled to match the geometry of blood vessels. Numerical results confirm the theoretical approach by referring to experimental data of different rat arteries.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 569-579 
    ISSN: 1069-8299
    Keywords: frictional contact ; large deformation ; one-pass approach ; master segment ; slave node ; contact constraint ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the context of large deformation analysis for metal forming processes a new one-pass approach for the frictional contact is proposed. This approach eliminates the short comings of traditional one-pass and two-pass approaches both from the constraint requirement and solution convergence points of view. Implemented in an updated Lagrangian framework with the Perturbed Lagrangian formulation of Ju and Taylor for non-linear frictional contact, a patch test and typical examples have been worked out to prove the validity of the proposed approach. It is observed that a finer surface discretization of the slave and master surfaces is no longer needed to enforce contact constraint.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
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    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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    Communications in Numerical Methods in Engineering 12 (1996), S. 595-595 
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    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Communications in Numerical Methods in Engineering 12 (1996), S. 599-608 
    ISSN: 1069-8299
    Keywords: finite elements ; moving grids ; moving bodies ; mesh velocity ; ALE ; Engineering ; Engineering General
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    Notes: A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 767-773 
    ISSN: 1069-8299
    Keywords: curved beam element ; membrane locking ; shear locking ; strain based element ; transformation matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two curved beam elements with two nodes and three nodes are designed based on strain fields. At the element level, curvature and membrane strain fields are approximated independently and shear strain fields are incorporated into the formulation by the equilibrium equations. The displacement fields are obtained by integrating the assumed strain fields. Two examples are given to verify the formulations and demonstrate the numerical performance of the two curved beam elements. Analysis results obtained reveal that the elements describe the curved beam behaviour correctly and show exceptional accuracy throughout a wide slenderness range.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 775-785 
    ISSN: 1069-8299
    Keywords: membrane ; wrinkle ; non-linear ; elasticity ; finite-element method ; sail ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigencomponents of the Cauchy stress tensor, which are solved by means of a secant method. The application of the element to sail design is presented in this paper.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 795-804 
    ISSN: 1069-8299
    Keywords: RLW equation ; finite element methods ; Petrov-Galerkin ; Engineering ; Engineering General
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    Notes: The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 787-793 
    ISSN: 1069-8299
    Keywords: regularization ; boundary integral equations ; hypersingular integrals ; Hadamard finite part ; Engineering ; Engineering General
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    Notes: Strongly singular integrals which are unbounded in the sense of Lebesgue appear naturally in boundary integral equations. Extending the analytic continuation method we derive finite part values for a class of singular integrals which arise frequently in practice. In connection with boundary integral operators we derive restrictions on the minimum smoothness of the density functions for the validity of the finite part results. Examples of applications of the results to boundary integral equations in potential theory are presented.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 805-805 
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    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996), S. 827-834 
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    Keywords: stress-strain relationship ; monotonic loading ; failure stress ; failure strain ; initial modulus ; Engineering ; Engineering General
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    Notes: A function containing four parameters allowing close approximation of experimental stress-strain relationships is presented. The parameters are easily determined from corresponding conditions at the ends and inside of the total interval of the strain variation from zero stain up to failure stain. The family of curves obtained covers an area on the stress-strain plane where any acceptable stress-strain curve can pass. The softening behaviour of soils can also be taken into consideration.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
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    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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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    Communications in Numerical Methods in Engineering 12 (1996), S. 835-847 
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    Keywords: superposition method ; perturbation of eigenvectors ; structural modification ; basis ofN-dimension Euclidean space ; orthogonalization of Schmit procedure ; Engineering ; Engineering General
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    Notes: The modal superposition method is often used for computing the perturbation of eigenvectors in structural modification and model correction. However, it will bring about significant errors in the solution when the high-frequency modes are truncated. This paper presents a new method, which uses known modes construct a new basis of the N-dimensional Euclidean space (say, the mixed-basis), to calculate the first and second order perturbations of the known eigenvectors. In the present method only the known modes are used. The accuracy of this method not only has no relation to number of the truncated modes but is better than the truncated modal superposition method, in which only the known modes are employed. A numerical example of a truss structure with 36 degrees of freedom is given to illustrate the effectiveness of the method.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 849-862 
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    Keywords: superconvergence ; isoparametric bilinear finite elements ; Engineering ; Engineering General
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    Notes: In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
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    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
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    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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    Communications in Numerical Methods in Engineering 12 (1996), S. 135-140 
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    Keywords: finite elements ; QUAD4 elements ; RBF corrections ; shear force predictions ; Engineering ; Engineering General
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    Notes: The residual bending flexibility correction is an extra-variational trick used to enhance the convergence rate of shear flexible beam and plate elements. In the paper we show how this can affect the shear deflection and shear force estimates in the QUAD4 element.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 597-597 
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    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996), S. 521-529 
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    Keywords: bellows ; shell of revolution ; integral equation method ; compressed angle ; Engineering ; Engineering General
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    Notes: In the paper a U-shaped bellows is treated as a flexible shell of revolution which consists of circular ring shells and truncated shallow conical shells; then the non-linear problem of U-shaped bellows under the action of axial compression force and internal pressure is solved by means of the non-linear theory of shells and the integral equation method. Numerical solutions obtained are compared with previous theoretical and experimental results. The present theory is more appropriate to the analysis of bellows in the light of real profile shape, and shows that the influence of compressed angle on the characteristic relation and peak stresses is noticeable.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 531-542 
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    Keywords: vibration ; inverse eigenvalue problem ; modal analysis ; Engineering ; Engineering General
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    Notes: A method for determining mass and stiffness modifications to achieve desired natural frequencies is presented. The given data are modal testing results, which consist of a truncated set of natural frequencies and mode shapes. The difficulty arising from the incompleteness of data is overcome by solving an optimization problem rather than seeking an exact solution. The obtained modifications are optimal in a Rayleigh-Ritz sense. The case where the mass and stiffness matrices are interrelated is also considered. Numerical examples demonstrating the various results and the sensitivity of the problem to perturbations are presented.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 609-616 
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    Keywords: hybrid-Trefftz element ; plate ; transient analysis ; Engineering ; Engineering General
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    Notes: The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 617-630 
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    Keywords: Engineering ; Engineering General
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    Notes: Three different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;- and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 631-641 
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    Keywords: numerical analysis ; fast direct method ; elliptic problems ; finite difference methods ; eigenvalue problems ; harmonic ; biharmonic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A high accuracy finite difference scheme has been developed for solving some elliptic problems which appear in engineering and applied sciences. These include Laplace, Poisson, Helmholtz and related equations. The second- and fourth-order problems dealing with vibration of membranes and plates have also been examined. Numerically, the problem reduces to a block tridiagonal system which can be solved by suitably modifying the fast direct method developed by Hockney. Comparison has been made with results obtained from some alternative numerical methods or analytical methods whenever available
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    Communications in Numerical Methods in Engineering 12 (1996), S. 643-655 
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    Keywords: viscoelastic flows ; sphere ; annular flow ; adaptive meshing ; finite elements ; error analysis ; Engineering ; Engineering General
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    Notes: This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 657-671 
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    Keywords: continuous casting ; free boundary problem ; co-ordinate transformation ; solidification front ; non-orthogonal control volume ; temperature profile ; Engineering ; Engineering General
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    Notes: An efficient computational simulation scheme based on non-orthogonal control volume discretization and co-ordinate transformation techniques has been developed for solving the thermal transport phenomena, which involves tracking of the interface between solid and liquid phases (solidification front) and evaluation of the temperature profile during continuous casting operation. Conservation equations are reformulated in differential-integral form in terms of the transformed co-ordinates. All the terms arising from the non-orthogonality of the control volume have been retained in the numerical solution methodology, and a front tracking procedure has been formulated based on an iterative solution scheme. The formulation has been applied to solve the thermal transport phenomena in solidification processing of an A1-Mg alloy cylindrical ingot during continuous casting, which also includes axial conduction of heat. Theoretical evaluation of the solidification front and temperature distribution in the ingot are in good agreement with the experimentally measured data.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 673-682 
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    Keywords: temperature field ; heat source ; IBEM ; Engineering ; Engineering General
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    Notes: The fundamental solution of the temperature field in an infinite three-dimensional body under the periodic unit thermal source is given in the present paper. According to the indirect boundary element method (IBEM) with fictitious heat sources, the problem of 3-D periodic heat conduction in a finite body is solved. By use of a quadratic inharmonic element, the problem of the corner region and the indetermination of the normal direction at boundary points can be solved in the numerical process. The validity of the present method is checked with two examples of which analytical solutions exist. It offers a useful method for the actual simulated calculation of the 3-D temperature field in engineering.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 703-703 
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    Communications in Numerical Methods in Engineering 12 (1996), S. 705-705 
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    Communications in Numerical Methods in Engineering 12 (1996), S. 707-717 
    ISSN: 1069-8299
    Keywords: hybrid element ; shear locking ; penalty-equilibrating approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper presents a penalty-equilibrating approach which is used to enforce the equilibrium constraints to individual hybrid elements so as to optimize the element performance. The approach has been applied successfully to improve the 4-noded hybrid stress membrane element (P-S) by Pian and Sumihara. It turns out that some defects of the P-S element, e.g. the shear locking phenomenon and the inability to pass the MacNeal's bending test, can be overcome and the element performance is significantly improved, without having to add any extra variables to the P-S element or to modify its stress fields.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 683-702 
    ISSN: 1069-8299
    Keywords: unstructured grid generation ; finite elements ; advancing front ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We describe extensions and improvements to the advancing front grid generation technique that have proven useful over the years. The following areas are treated in detail: situations with thin or crossing surfaces, meshing of surfaces defined by triangulations, and ease of user input to define the desired element size in space. The first extension is important if one considers the generation of volumetric grids around shells, membranes, fabrics, or CAD-data that exhibit cusps. Traditional advancing front generators are likely to fail in these situations. We propose the introduction of a crossing environment variable attached to faces and points in order to filter out undesired or incorrect information during the grid generation process. The second extension is required for situations where the surfaces to be gridded are not defined analytically, but via a triangulation. Typical cases where such triangulations are used to define the domain are geophysical problems, climate modelling and medical problems. The third topic deals with the reduction of manual labour to specify element size in space. Sources, element size attached directly to CAD-data, and adaptive background grids are discussed. Adaptive background grids, in combination with surface deviation tolerances, are used to obtain surface triangulations that represent the geometry faithfully, and at the same time enable a smooth transition to volumetric meshes.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 731-743 
    ISSN: 1069-8299
    Keywords: explicit integration ; finite elements ; stiffness matrix ; symbolic manipulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 719-729 
    ISSN: 1069-8299
    Keywords: air humidification process ; experiments ; predictions with finite-difference technique ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a numerical and an experimental analysis of the humidification process of air in a nearly horizontal tube. The numerical analysis is based on a finite-difference solution of the three-dimensional momentum, heat and mass transfer differential equations within the tube for the evaporation process of a water stream of circular meniscus cross-section counterflowing to an air stream. In order to provide reliable, high-accuracy data to assist in the development of the theoretical model, tests have been conducted using specially constructed apparatus to measure temperature and velocity profiles within the tube. The proposed computer algorithm was validated by evaluating its ability to predict the measurements of temperatures and velocities along the stream's flow. The theoretical predictions agree well with the experimental data. The model may be used to give performance characteristics for a wide range of humidification processes with different working fluids and state conditions.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 745-753 
    ISSN: 1069-8299
    Keywords: boundary element method ; foundations ; soil-structure interaction ; contact problem ; optimal solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of providing settlement uniformity of a rigid foundation on a non-uniformly compressible base has been reduced to the contact problem from elasticity theory, with controlling parameters which allow one to select either co-ordinates of the point of application of the vertical load resultant or contours in plan at which the foundation slope will be equal to zero. The solution of the problem is illustrated by numerical examples.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 755-766 
    ISSN: 1069-8299
    Keywords: finite elements ; isoparametric ; Jacobian ; transformation ; valid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Isoparametric elements are only valid if the Jacobian determinant of the transformation between a given element and a master element does not change sign within or on the element boundary. Some algorithms are known which analyse Jacobians for various element types. Some necessary conditions are presented for determining the validity of an element.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 885-896 
    ISSN: 1069-8299
    Keywords: interfaces ; sliding ; contact ; impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automatic sliding interface algorithm for intense impulsive loading computations due to high velocity impact and explosive detonation. This algorithm allows the user to perform computations involving complex sliding interfaces without having to predetermine the sliding interfaces; everything is automated. The interface determination algorithm, the searching algorithm and the contact algorithm are included.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 863-871 
    ISSN: 1069-8299
    Keywords: objectivity ; kinematics ; computational mechanics ; large deformations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an example problem is presented that illustrates the importance of strong objectivity in kinematic algorithms for large-deformation finite element applications. The example problem involves cyclic simple shearing of a hypoelastic material, wherein the increments of stretch and of rotation are of comparable magnitude. It is demonstrated that two kinematic algorithms that are in common use, and which are only weakly objective, give rise to an accumulative error in the normal stress components. The error is surprisingly large, even for very small strain increments. This behaviour arises due to a coupling between the stretch and rotation increments that is exhibited by weakly objective algorithms, and is perhaps especially serious in the context of models for jointed rock and other frictional materials, in which the shear response may depend strongly on the normal components of stress.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 905-905 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996), S. 897-903 
    ISSN: 1069-8299
    Keywords: finite element analysis ; reinforced concrete element ; embedded reinforcement ; stress analysis ; brick element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1-32 
    ISSN: 0029-5981
    Keywords: finite volumes ; finite elements ; compressible flows ; unstructured grids ; hybrid grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 81-97 
    ISSN: 0029-5981
    Keywords: porous media ; mixture theories ; fluid-saturated binary model ; incompressible constituents ; non-linear elasticity ; dynamic loading ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 141-163 
    ISSN: 0029-5981
    Keywords: induction heating ; coupled problem ; three-dimensional analysis ; eddy current temperature analysis ; thin conducting sheet model ; eddy current boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a special finite element formulation for the computer simulation of an inductive heating device for thin moving metal strips. The calculation includes both the electromagnetic field and the temperature distribution resulting from the losses of the induced currents. The electromagnetic field is described by an electric vector potential and a magnetic scalar potential, the induced eddy currents are represented by a special boundary condition for the magnetic scalar potential along the surface of the current-carrying strip. This avoids the necessity to discretize the thin secondary region. The thermal model includes the movement of the strip as well as convection and radiation as its surfaces. The field equations are discretized using the Galerkin variant of the Method of Weighted Residuals. The mutually coupled electromagnetic and temperature fields are then calculated using an iterative, staggered solution scheme. Comparisons between calculated and measured temperature profiles show the validity of the presented approach.
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    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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    International Journal for Numerical Methods in Engineering 39 (1996), S. 165-184 
    ISSN: 0029-5981
    Keywords: curved unilateral contact ; augmented Lagrangian ; frictional contact element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a mixed formulation approach, a frictional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified.For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed.Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1097-1114 
    ISSN: 0029-5981
    Keywords: finite elements ; pneumatics ; air springs ; containers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surrounding structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtual boundary work done by the pressure of the enclosed gas. The augmented equations are discretized using standard finite element methods, and the additional terms are discussed. The resulting ‘pneumatic’ finite element is shown to be analogous to regular structural finite elements. To assess the accuracy and efficiency and also to illustrate the applicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a partially filled plastic food product container is studied. The numerical results using the pneumatic element compare well with an alternative Rayleigh-Ritz solution of the end cap behaviour. The other two examples represent the behaviour of a double bellows air spring shock absorber under static isothermal and dynamic adiabatic conditions. For the static isothermal case, an experimental study was performed with results in good agreement with the pneumatic element solutions. For the dynamic adiabatic loading case, the dynamic stiffness of the air spring was predicted using the pneumatic element. The numerical results agree with experimental data published in an air spring application guide. The examples illustrate that the pneumatic element formulation can be applied to the large deflection analysis of structures that enclose gas filled volumes.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1115-1136 
    ISSN: 0029-5981
    Keywords: particle tracking ; Lagrangian-Eulerian finite element methods ; Engineering ; Engineering General
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    Notes: This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian-Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian- Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1313-1340 
    ISSN: 0029-5981
    Keywords: iterative methods for linear systems ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1341-1356 
    ISSN: 0029-5981
    Keywords: constrained optimization ; feasible descent ; mathematical programming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new Feasible Descent Cone (FDC) method for constrained optimization, previously restricted to linear objectives, is here generalized to include non-linear objective functions as well. In the basic and exact algorithm a sequence of descent steps is taken through the interior of the feasible region along the central lines of mathematically defined descent cones, constructed at successive boundary points. Here the basic algorithm is modified to allow for a minimum to occur within the interior, along a central descent ray in the case of non-linear objectives. A special interior procedure, with desirable mathematical properties, is adopted should the latter occur. To ensure economic implementation, the new generalized and exact algorithm, referred to as SSOPT2, is successively applied to a sequence of approximate quadratic subproblems. The overall generalized procedure that includes the successive application of SSOPT2 to the approximate subproblems, is referred to as the successive approximation version 2 algorithm (SAM2). The practical performance of SAM2 is assessed through its application to a number of small but otherwise representative test problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1357-1382 
    ISSN: 0029-5981
    Keywords: numerical reduced minimization ; non-uniform isoparametric mapping ; unmatched coefficient ; spurious constraint ; optimal minimization ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the effects of various numerical integrations on the behaviour of C0-continuous beam elements under non-uniform isoparametric mapping are investigated by using numerical reduced minimization theory. The theory shows that stress recovery can be achieved by sampling stresses at the optimal integration points once a reduced integration is employed. It rationalizes the continued acceptance of the conventional reduced integration of constrained strain energy as one of remedies for locking due to spurious constraint.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1383-1403 
    ISSN: 0029-5981
    Keywords: crashworthiness ; homogenization ; topology design ; automotive structure optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density.Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored.The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1419-1431 
    ISSN: 0029-5981
    Keywords: integral equations ; scattering ; boundary elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a boundary integral equation (boundary element) method for the solution of a variety of transient acoustic problems. The spatial and temporal discretization employs quadratic isoparametric elements with high-order Gauss quadrature, and the ensuing equations are implicit. The implicit formulation both eliminates the instabilities reported in explicit treatments, and permits a freedom of choice of timestep which can reduce costs dramatically. The accuracy of the approach is demonstrated by comparison with the analytical solution for a sphere. Results for more demanding sphere-cone-sphere geometries extending to seven wavelengths long are presented, and compared to those obtained from a related frequency domain approach.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1405-1417 
    ISSN: 0029-5981
    Keywords: RTM ; control volume ; free surface ; porous medium ; sparse matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An efficient numerical scheme is presented for simulating isothermal flow in resin transfer molding. The problem involves transient, free surface flow of an incompressible fluid into a non-deforming porous medium. A new variant of the Control Volume Finite Element (CVFE) algorithm is explained in detail. It is shown how the pressure solutions at each time step can be obtained by adding a single row and column to the Cholesky factorization of the stiffness matrix derived from a finite element formulation for the pressure field. This approach reduces the computation of a new pressure solution at each time step to essentially just two sparse matrix back-substitutions. The resulting performance improvement facilitates interactive simulation and the solution of inverse problems which require many simulations of the filling problem. The computational complexity of the calculation is bounded by O(n2⋅5), where n is the number of nodes in the finite element mesh. A 100-fold speedup over a conventional CVFE implementation was obtained for a 2213-node problem.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1436-1436 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1433-1435 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1437-1454 
    ISSN: 0029-5981
    Keywords: large elastic deformations ; enhanced strain method ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1455-1473 
    ISSN: 0029-5981
    Keywords: transient loads ; advective-diffusive equations ; Petrov-Galerkin ; Galerkin Leask-Square ; boundary layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective-diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least-Square method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1475-1489 
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    Keywords: meshing ; three-dimensional ; surfaces ; quadrilateral ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three-dimensional trimmed surfaces. Methods of calculating angles, projecting elements, and detecting collisions between paving boundaries, for general surfaces are presented. Extensions of the smoothing algorithms for three dimensions are set forth. Advances in the use of scalar sizing functions are presented. These functions can be used to better approximate internal mesh density from boundary densities and surface characteristics.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2155-2168 
    ISSN: 0029-5981
    Keywords: buckling ; composite laminated structures ; high-order element ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new high-order element for prebuckling and buckling of any laminated plane frame is developed. The kinematic approach involves a variety of high-order models with different powers of the thickness co-ordinate, and the derived stiffness matrix is based on a special power series, without a numerical process. It yields an exact formulation for high-order (first) models and improved formulations for higher-order (second and third) ones. A parametric study of the ‘locking’ phenomenon and the shear deformation effects was carried out for isotropic and laminated structures. It was found that the first-order model with an appropriate shear correction factor yielded results close to its higher-order counterparts.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 199
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2265-2282 
    ISSN: 0029-5981
    Keywords: energy-conservation ; dynamics ; beams ; co-rotation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes an energy-conserving procedure for the implicit non-linear dynamic analysis of planar beam structures. The method is based on a form of co-rotational technique which is ‘external to the element’. A range of numerical results are presented which clearly demonstrate the improved numerical performance in comparison with more conventional techniques.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 200
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2555-2573 
    ISSN: 0029-5981
    Keywords: 3-D boundary element method ; elastoplastic analysis ; hypersingular formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3-D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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