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  • Articles: DFG German National Licenses  (565)
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  • Articles: DFG German National Licenses  (565)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 171-181 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The study of the deviation of a crack reaching the interface separating two materials in a multilayer in a 4-point deflection is considered. This study is based on the use of special isoparametric finite elements.1 (The elements surrounding the crack tip have nodes placed at a distance α from the crack tip, and in this way we impose a singularity of the stresses in the neighbourhood of the crack.)The Erdogan2 criterion that estimates the deviation angle shows that this angle is a function of the initial angle of the crack, and the properties of each component of the multilayer.
    Additional Material: 17 Ill.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 255-274 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin method for the solution of the compressible Euler and Navier-Stokes equations is presented. It is based on the introduction of an anisotropic blancing diffusion in the direction of the local direction of propagation of the scalar variables. The local direction in which the anisotropic diffusion is introduced is uniquely determined, and the magnitude of the balancing diffusion is automatically calculated locally using a criterion that is optimal for one-dimensional transport equations.The algorithm has been implemented using four-noded bilinear elements with forward Euler and second-order Runge-Kutta methods of integration in time. Several applications are presented and show the stability and approximation properties of the method.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 969-990 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite-spectral elements and finite wave elements are developed. Finite-spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.
    Additional Material: 9 Ill.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 991-1008 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computationally advantageous multi-domain boundary element formulation is presented for uncoupled thermoelastic analysis of two- and three-dimensional isotropic media. Particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed. These particular integrals are derived using an orderly approach. When temperature data are provided at discrete points, the best fit quadratic distribution is generated in the least square error sense which, together with a multi-domain approach, makes it possible to represent an arbitrary temperature distribution within acceptable bounds. Numerical examples are given to show the efficiency and effectiveness of the present formulation, which is now incorporated in a general purpose boundary element code named GPBEST.
    Additional Material: 10 Ill.
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1009-1026 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Application of the two-sided Lanczos recursion to the unsymmetric generalized eigenvalue problem is presented. The system matrices are real and unsymmetric. Therefore, the recursions are performed in real arithmetic and complex arithmetic is employed in the QR algorithm used to extract the eigenvalues of the transformed tridiagonal matrix. The biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in Appendices. Issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed. The example problems solved demonstrate the working of the algorithm in extracting the complex and/or real eignevalues of an unsymmetric system of matrices. Also, the algorithm is applied to extract a few of the eigenvalues of a large fluid-structure interaction problem, and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature.
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1205-1227 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.
    Additional Material: 12 Ill.
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1267-1281 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present, discuss, and report on the performance of two combined parallel/vector frontal algorithms which have been incorporated in a production finite element code. Two parallelization strategies are described. The first approach is algebra driven and is recommended for the solution of problems with a large bandwidth on a coarse grain configuration. The second strategy is targeted for finer grain systems; it blends the first one with a substructuring technique that is based on a careful partitioning of the finite element mesh into a series of subdomains. Using only 4 IBM 3090/VF processors, the proposed algorithms are shown to deliver speed-ups as high as 17 with respect to a serial non-vectorized frontal solver.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1247-1265 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method to analyse stochastic design sensitivity for problems of structural dynamics is presented. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element context. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations exicited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition technique: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient; they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. A number of numerical results for the deterministic and stochastic sensitivity analysis of beams and shells illustrates the paper.
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  • 109
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1283-1301 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive mesh refinement (AMR) procedure is used in static thin shell analysis using triangular facet shell elements. The procedure described herein uses the h-version of adaptive refinement based on an error estimate determined by using the best guess values of bending moments and membrane forces obtained from a previous solution. It includes the use of a relaxation factor to achieve better convergence. Some examples are presented to illustrate this method. The results obtained are compared with those of uniform mesh refinement (UMR).
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1303-1319 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is developed and tested for the numerical solution of the three-dimensional convection - diffusion equation appropriate for the marine environment, in which the horizontal and vertical scales differ by one or two orders of magnitude. The algorithm splits the horizontal and vertical parts of the process, treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable. The overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known.
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1365-1368 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1321-1337 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.
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  • 113
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1339-1361 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient method, based on the Schwarz-Neumann alternating technique, is presented for computing weight functions of a general solid (3-D as well as 2-D), with embedded or surface-flaw configurations. The total rate of change of the crack-opening displacements, due to simple perturbations of crack-dimension characteristics, is conveniently decomposed into the infinite-domain and boundary-correction parts. The former is determined from available analytical solutions of ideal-shaped cracks, whereas the latter is computed numerically by imposing nil boundary-traction requirements for the displacement field corresponding to the weight functions. Numerical examples, with solutions for 3-D weighted-average and local stress intensity factors, indicate that the proposed method is very accurate and efficient.
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1369-1370 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1427-1451 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The computation of the three-dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds-Averaged Navier-Stokes Equations written in a non-orthogonal curvilinear body-fitted co-ordinate system. Results of the computation are compared with available experiments.
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  • 117
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 118
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1471-1474 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1475-1476 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 120
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1476-1476 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 121
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 651-651 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 122
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 123
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 665-675 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The reconstruction of a solid surface from a series of cross-sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications. We describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points. A simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior.
    Additional Material: 10 Ill.
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  • 124
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 653-663 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In recent years, numerical analysts have increasingly turned to adaptive-grid techniques to efficiently obtain highly-accurate solutions to partial-differential equations. This paper presents a comparison of two distinct grid-adaptation approaches, grid-point redistribution and grid-embedding, applied to two-dimensional, steady, inviscid, shocked flows. Grid redistribution is accomplished through a control function approach applied to the elliptic-grid generator while the embedding approach consists of a fixed global grid and an automatically chosen number of irregularly shaped, embedded regions. For both techniques, the Euler flow equations are integrated to steady state using Ni's Lax-Wendroff-type integrator to predict the flow fields about a variety of isolated airfoil configurations. The application of a common integration scheme as well as a common adaptive control function leads to a direct comparison of the effectiveness of the two adaptation approaches for the types of problems tested.
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  • 125
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 677-707 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the hyperbolic systems of equations governing transient acoustics by adaptive finite elements and various finite difference time discretization schemes is addressed. Emphasis is placed on the use of a class of implicit Runge-Kutta methods for temporal approximations.
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  • 126
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 709-749 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An octree-based fully automatic three-dimensional mesh generator is presented. The mesh generator is capable of meshing non-manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The resulting procedure demonstrates a linear growth rate with respect to the number of elements and can be easily integrated with any geometric modeller through a set of geometric operators.
    Additional Material: 34 Ill.
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  • 127
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 751-765 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries. The method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration, using an error estimation procedure coupled to an automatic triangular mesh generator. Two numerical examples are included to illustrate the numerical performance of the method.
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  • 128
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 767-781 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An error estimation technique for adaptive finite element analysis of heat conduction problems is described. The performance of this technique is demonstrated using a two-dimensional steady-state linear benchmark problem with a known analytical solution. A transient non-linear heat conduction problem involving solidification is then solved as a typical practical application. Some preliminary investigations for error indicators in flow problems are presented.
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  • 129
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 811-847 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new mesh generation technique, paving, which meshes arbitrary 2-D geometries with an all-quadrilateral mesh. Paving allows varying element size distributions on the boundary as well as the interior of a region. The generated mesh is well formed (i.e. nearly square elements, elements perpendicular to boundaries, etc.) and geometrically pleasing (i.e. mesh contours tend to follow geometric contours of the boundary). In this paper we describe the theory behind this algorithmic/heuristic technique, evaluate the performance of the approach and present examples of automatically generated meshes.
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  • 130
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 783-810 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success.Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement.With h and h-p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density.The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.
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  • 131
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 867-893 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automated, adaptive finite element modelling system based on the hp-version of the finite element method. Error estimation and correction indication procedures with an automatic mesh generator and a p-version analysis code are combined to provide a computationally efficient modelling environment. Error prediction techniques are employed to find the best combination of finite element discretization, h-, and overall polynomial order, p-, needed to achieve the prescribed level of accuracy. The automated adaptive modelling results demonstrate the capability of the modelling system of predicting discretizations to perform a p-version finite element analysis to achieve prescribed levels of accuracy in the most efficient manner.
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  • 132
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 849-866 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.
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  • 133
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 939-941 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 134
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    International Journal for Numerical Methods in Engineering 32 (1991) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 135
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 895-919 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structured meshes which consist of a single curvilinear network of lines and points have limited flexibility when applied to geometrically complicated domains. To alleviate this constraint the idea of multiblock structured meshes has been proposed. This approach subdivides the domain of interest into regions, each of which can be mapped into a transformed space equivalent to a rectangle. The connections between these regions define the mesh topology. By a suitable subdivision of the domain, multiblock grids, which are globally unstructured between blocks, but provide a structured grid within blocks, can be used to discretize highly complex geometrical domains. This technique has been used to great effect, both in two and three dimensions. However, structured meshes are not naturally amenable to adaptivity techniques based upon local point addition. This paper describes a method, based upon the quadtree data structure, which allows for local point refinement on multiblock meshes for use with flow algorithms for the simulation of compressible flow around aerospace geometries. The basic concepts of multiblock meshes, the use of the quadtree data structure, together with the treatment within the flow algorithm of locally embedded meshes, will be discussed.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 943-955 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free-vibrational responses of linear, undamped, single-degree-of-freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 369-384 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced level development of the boundary element method is presented for the elastic stress analysis of a three-dimensional solid containing a large number of small diameter, tubular shaped holes. The formulation has been developed such that these holes can be modelled by a system of curvilinear line elements, resulting in substantial savings in both data preparation and computing costs. This is accomplished by assuming a variation in the displacement field along the circumference defined in terms of trigonometric functions together with a linear or quadratic variation of displacements along the longitudinal direction.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 345-367 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 463-491 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We have developed a finite element method for analysing non-linear and linear fluid-structure interaction problems by working directly from a variational indicator based on Hamilton's principle. We restrict our analyses to inviscid, irrotational and isentropic fluid flows. The variational indicator includes the fluid potential energy due to gravity, which is often ignored. This and the fact that we consider our domain to be variable provide us with the capability to model free surfaces.We demonstrate the effectiveness of both linear and non-linear finite element formulations in analysing a variety of fluid-structure interaction problems.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 819-820 
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  • 141
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    International Journal for Numerical Methods in Engineering 31 (1991) 
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  • 142
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 821-824 
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  • 143
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 803-817 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Boundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 825-835 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper considers various procedures that yield improved stiffness matrices for plane triangular elements. Each element has nine d.o.f. and vertex nodes only. Some of the resulting elements are non-classical constant strain triangles while others have more competent displacement fields. Numerical examples suggest that the nine-d.o.f. element can either be formulated more efficiently or made more accurate, but probably not both at the same time.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 837-857 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The finite strip method is extended to the non-linear, static analysis of cylindrical shells. Large deflection effects are incorporated via first-order non-linearities in the strain-displacement relations, and material non-linearities are included via the von Mises yield criteria and associated flow rule. Numerical results are presented for various example problems including the diaphragm supported cylindrical shell-roof problem, an axisymmetric cylindrical shell loaded by radial pressure, the cylindrical shell-roof problem with clamped curved ends and a pressure loaded cylindrical panel clamped all round. The results are compared with known results from analytical and/or finite element analyses. The results indicate that a single bending mode in the strip direction is sufficient in most cases to yield engineering accuracy for preliminary design purposes.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 879-894 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 987-997 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The Delaunay triangulation has been used in several methods for generating finite element tetrahedral meshes in three-dimensional polyhedral regions. Other types of three-dimensional triangulations are possible, such as a triangulation satisfying a local max-min solid angle criterion. In this paper, we present experimental results to show that max-min solid angle triangulations are better than Delaunay triangulations for finite element tetrahedral meshes, since the former type of triangulations contains tetrahedra of better shape than the latter type. We also describe how mesh points are generated and triangulated in our tetrahedral mesh generation method.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1027-1030 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 999-1008 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This article discusses two alternative methods of formulating the recently proposed quadrilateral plane element Qcs6, which is based on a generalized functional with multiple stress fields. The first method is derived by an extended Hu-Washizu Principle with the presence of incompatible modes and enforcement of energy orthogonality, while the second one is established on a non-conventional discrete local stress smoothing. Both methods can be applied to other structural element formulations with enhanced efficiency.
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    International Journal for Numerical Methods in Engineering 31 (1991) 
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1009-1026 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Scattering of elastic plane waves by three dimensional non-axisymmetric multiple dipping layers embedded in an elastic half-space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square sense at points on the layer interfaces and on the surface of the half-space. The transient response is constructed from the steady state solution by using Fourier synthesis.Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non-axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1031-1054 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non-linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate-insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non-linear solution algorithm has traditionally hampered their use.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1691-1710 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method based on finite elements, characterized by generalized strains as functions of the nodal co-ordinates, is the basis for the computer program SPACAR for the kinematic and dynamic analysis of flexible multibody systems. This program allows also the evaluation of the linearized dynamical equations, which makes possible the implementation of a method for the direct determination of stationary and periodic solutions and of a continuation method for these solutions if some parameter is varied. As an illustration, these methods are applied to a Duffing equation, a double pendulum and a slider-crank mechanism with an elastic connecting rod.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1711-1725 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper we present a general procedure for analysing the motion of a multi-rigid-body system that is capturing and/or ejecting mass. The motivations for this work are given in the introductory section, followed by a description of the mathematical model we have used to represent a variable-mass system. Using a control volume approach, the differential equations of motion are derived in vector-dyadic form. The non-linear scalar components of these equations have been encoded into a Fortran-77 program that uses a fourth-order Runge-Kutta algorithm to compute a numerical solution for the motion of a given physical system; we describe the development of this simulation program and its use of the conformal rotation vector to represent orientations. An application of the program to the dynamic analysis of a specific variable-mass problem is presented, and a comparison of the numerical results to an analytical solution is used to assess the accuracy of the software. In the concluding section, the advantages and limitations of the underlying formulation are discussed.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1727-1748 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A relatively general formulation for studying the dynamics of an arbitrary spacecraft with interconnected flexible bodies is developed accounting for thermal deflection, transient system inertias, shift in the centre of mass, shear deformations, rotary inertias and geometric non-linearities. The computer implementation has been carried out through symbolic manipulation of the equations of motion. Versatility of the formulation is indicated through application to problems of contemporary interest.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1749-1766 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A systematic method for formulating the equations of motion for multibody systems containing rigid and flexible bodies is presented. The method of using joint co-ordinates to derive the minimum number of equations of motion is utilized for rigid bodies and the finite element method is employed for flexible bodies. The equations of motion for flexible bodies are simplified into several steps using (a) a lumped mass assumption, (b) static condensation and (c) modal superposition. The combined rigid and flexible body formulation can be used to simulate dynamic response in a variety of applications such as ride handling, rollover and the crash analysis of vehicles, space structures, and biomechanical problems.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1767-1798 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A computationally oriented formulation and its solution procedures for the analysis of rigid-flexible multibody dynamics systems are presented. The present formulation adopts a set of dual co-ordinate systems, an inertially fixed one for the measure of translational motions and a body-based one for rotational motions. The origins of these co-ordinate systems are located at the centres of rigid bodies and at the nodal points of flexible bodies for implementation ease. The flexibility is modelled by an intrinsic spatial beam theory which is approximated by transverse-shear deformable linear beam elements. The solution of the resulting equations of motion including system constraints is obtained by a partitioned procedure, which solves first for the constraint force vector, then the generalized co-ordinates for the rigid and flexible components, and finally interaction quantities such as active control forces, manoeuvring space ranges and corrections due to state measurements, with each solution stage being processed by the corresponding separate module. A central feature of the present capability is its high accuracy of the analysis results by demanding the energy conservation throughout the various stages of response analyses. Several examples are included to demonstrate the capabilities of the present analysis software both on sequential and parallel machines.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1683-1686 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 207-209 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 183-205 
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    Notes: A fast algorithm is presented for constructing continuous lines, made up of element sides, which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions. The lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two-dimensional problems of steady compressible inviscid and laminar viscous high-speed flows, where the equation system is solved by line relaxation using a block tridiagonal equation solver. For three-dimensional laminar viscous simulations it is proposed to utilize an implicit/explicit finite-element formulation. In the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while, away from this region, the grid will be totally unstructured. In the structured region, lines in the normal direction to the wall are readily identified, while lines in the surfaces parallel to the solid wall are constructed using the proposed two-dimensional procedure. The implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation. An explicit form of the solution algorithm is used elsewhere. To illustrate the performance of the proposed method, solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions. The application of the proposed procedure to the solution of three-dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 213-213 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 217-218 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 313-325 
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    Notes: Boundary integral approaches, which are known for their mathematical sophistication and elegance as well as their ability to reduce the problem dimensions by one, suffer from drawbacks associated with their performance in the vicinity of the boundaries. Such behaviour is the result of the unavoidable, in most cases, discretization of the boundary on one hand, which consequently results in the reduction of the integral problem to an algebraic one, and of the tedious evaluation of singularities that are present in most kernels on the other. The sensitivity of solutions of shell problems using a special form of boundary integral method is studied. Such an approach hopes to achieve a better representation of the solution near the boundaries by utilizing fictitious surface lines to perform the kernel integrations. Lastly, the performance of the integral formulation is examined through some representative examples.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 327-346 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A large variety of design optimization methods have been proposed in recent years. Comparison of the relative performance of each method is a difficult task, and attempts to do so are often based on a limited number of numerical experiments. Recently, a ‘basins of attraction’ construction has been proposed as a graphical tool for investigating global performance of iterative design optimization methods, and as a basis for comparison of different methods. The phase-space representation presented in this paper is a companion to the basins of attraction construction. Basins of attraction reveal the relationship between starting design and final outcome of the solution process; the phase-space construction reveals that nature of the paths connecting the starting design and final outcome. The two constructions complement one another in summarizing the performance of design optimization processes. Both constructions are demonstrated in this paper, applied to the optimal design of an elastic grillage structure using Newton's method and the stress ratio method.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 347-362 
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    Notes: A study is conducted of the finite element solution of elliptic partial differential equations on a data parallel computer. A nodal assembly technique is introduced which maps a single node to a single processor. The system of equations is first assembled and then solved in parallel using a conjugate gradient algorithm for unsymmetric, non-positive definite systems. Using this technique and a massively parallel machine, problems in excess of 100k nodes are solved.Results of electromagnetic scattering, governed by the 2-d scalar Helmholtz equation, are presented for both an infinite cylinder and an airfoil cross-section. Solutions are demonstrated for a wide range of object sizes. A summary of performance data is given for a set of test problems.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1093-1113 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour.For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.
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  • 168
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1115-1135 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new rectangular finite element for moderately thick plates is presented. The element is based on the concept of physical shape functions, i.e. functions which contain in themselves physical and geometrical properties of the element. The analytic formulae of stiffness, geometric stiffness and mass matrices are presented for isotropic material. The element is free from locking and zero energy modes not corresponding to rigid body motions.Several examples are presented for static, initial stability and free vibration problems.
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  • 169
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1145-1159 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive finite element method for the solution of time dependent strongly compressible flows in two dimensions is described. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Problems involving shock propagation are solved to illustrate the numerical performance of the proposed approach.
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  • 170
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1229-1245 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard formulae of the fourth order Runge-Kutta method are transformed into a finite difference equation which allow us to solve linear boundary value problems. This equation is manipulated further and extended into 2D for solving second order linear partial differential equations. The various transformations result in four equations for the two first derivatives, mixed second derivative and the function value in the depicted point of the mesh. Each of these quantities is expressed by the linear combination of values of the function given in the eight nearest nodes around the depicted node. Explicit formulation of the equations for corner, boundary, symmetry and internal nodes is given. The results of the new computer code are compared with an analytical result and precise measurements, as well as a FEM calculation. It is concluded, for the specific example investigated, that the new method is about ten or more times precise than the FEM with the same number of elements. The major merit of the method lies in the fact that it can be implemented on personal computers.
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  • 171
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1319-1331 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient formulation is presented to predict the buckling under combined loading of relatively long shear deformable laminated anisotropic plates. The numerical formulation is based on a semi-analytical Reissner-Mindlin ‘infinite’ strip. The effect of shear locking is eliminated by the use of higher Lagrangian polynomials. The deterioration of Kirchhoff theory (classical plate theory (CPT)) in the case of moderately thick anisotropic plate is highlighted. A complete convergence study of the present theory was carried out and the accuracy of the method is demonstrated by comparison with the published results.
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  • 172
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1333-1356 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Numerical experiments in adapting variations of a computationally simple error estimator (the Zienkiewicz-Zhu estimator) to an existing finite element code are shown. The error estimator used allows both overall and local errors to be estimated. From the local estimates of error, refinements of the mesh are calculated to reach a prescribed error tolerance. These calculated refinements are used by a mesh refiner to produce a modified mesh which lowers the overall error to the prescribed value while keeping the mesh as crude as possible. The physical example on which these numerical experiments are performed is that of free surface flow through an earth dam with a toe drain. It is also shown how the problem formulation affects the error analysis and how the choice of computational scheme affects the mesh adaptation.
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  • 173
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1357-1374 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the solution of the three basic semiconductor equations in two space dimensions fully self-adaptive grids are a powerful tool to optimize the ratio between the number of unknowns and the accuracy of the solution. For the method of finite differences hardly any mathematically founded criterion for automatic grid control can be given which can be implemented in a computer program with acceptable effort. Therefore most of the strategies for self-adaptive grid control are totally heuristic or derived from physical properties.In this paper we present criteria for the design of an initial space grid. We discuss some conventional strategies for the automatic control of space grids (e.g. equidistribution of the local discretization error) and present new criteria (e.g. degree of coupling of the equations, physical properties like net generation rate). For the time grid an automatic step length control algorithm is presented and the interaction between space and time grid is analysed. Throughout the paper the results are illustrated by realistic examples.
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  • 174
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1375-1392 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element based method is presented for evaluation of linearized dynamic equations of flexible mechanisms about a nominal trajectory. The coefficient matrices of the linearized equations of motion are evaluated as explicit analytical expressions involving mixed sets of generalized co-ordinates of the mechanism with rigid links and deformation mode co-ordinates that characterize deformation of flexible link elements. This task is accomplished by employing the general framework of the geometric transfer function formalism. The proposed method is general in nature and can be applied to spatial mechanisms and manipulators having revolute and prismatic joints. The method also permits investigation of the dynamics of flexible rotors and spinning shafts. Application of the theory is illustrated through a detailed model development of a four-bar mechanism and the analysis of bending vibrations of two single link mechanisms in which the link is considered as a rotating flexible arm or as an unsymmetrical rotating shaft, respectively. The algorithm for the calculation of the matrix coefficients is directly emenable to numerical computation and has been incorporated into the linearization module of the computer program SPACAR1.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1393-1414 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Thick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields. Both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node. Performance of the elements is evaluated on a set of problems in elastostatics. However, the formulation presented herein is also suitable for transient and non-linear problems.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1415-1426 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Three algorithms for draping biaxially woven fabrics on arbitrarily curved surfaces are presented and compared for numerical accuracy and computational expense. The first one minimizes the elastic energy in each fabric cell, while the two others are based on placing a net of interlocked and inextensible fibres on the surface along geodesic lines. A benchmark shows that the minimum energy technique performs the best and is also the most promising for further optimization in terms of numerical quadrature formulae.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1469-1470 
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    International Journal for Numerical Methods in Engineering 31 (1991) 
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1-17 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A searching algorithm is presented for determining which members of a set of n points in an N dimensional space lie inside a prescribed space subregion. The algorithm is then extended to handle finite size objects as well as points. In this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object. The suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 53-66 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The objective of this paper is to present a method of causal FFT treatment which is available to not only approximately time-limited and band-limited functions but also singularity functions appearing frequently in earthquake engineering problems such as time domain response analyses and seismic record processing. By means of the causal FFT treatment for a singularity function, it is possible to determine several causal functions. The properties of the obtained causal functions are discussed in detail. The 0 second and 0 Hz value problems of engineering importance concerning the determination of the discrete singularity values of non-time-limited or non-band-limited functions are presented. Finally, by presenting numerical examples, several problems existing in the FFT analyses of singularity functions and a method to solve the problems are explained in detail.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 67-84 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is presented for the fully automatic conversion of a general finite element mesh containing triangular elements into a mesh composed of exclusively quadrilateral elements. The initial mesh may be constructed of entirely triangular elements or may consist of a mixture of triangular and quadrilateral elements. The technique used employs heuristic procedures and criteria to selectively combine adjacent triangular elements into quadrilaterals based on preestablished criteria for element quality. Additional procedures are included to eliminate isolated triangles. The methods operates completely without user intervention once the nodal co-ordinates and element connectivity of the original mesh are supplied.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 241-263 
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    Notes: A geometrically non-linear constant moment triangular finite element is designed under Kirchhoff theory from a Hu-Washizu functional such that it passes the totality of von Kármán patch tests for constant strain and constant curvature. The non-linear triangle has the same connection properties as in the linear theory where the constant strain triangle is superposed upon the displacement version of the constant moment triangle.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1565-1593 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non-linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1621-1635 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The aim of this paper is to present the equations of motion of deformable multi-body systems in a compact form which is suitable for symbolic generation. Particular attention is paid to obtaining the various equations corresponding to joint displacements and body deformations in a unified manner. A large number of common intermediate terms are identified and appropriately assembled in the final form of the equations; for the various applications, this simple consideration permits one to drastically save on the computational effort. This paper also presents the data which are necessary to completely formulate the problem when the body deformations are described by a linear elasticity model (obtained from a modal or finite element description).
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1595-1619 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The object of this paper is to present a study on the modelling and control of flexible robots by using a knowledge based control design approach. We first develop an appropriate model of such a mechanical system in the case of open loop robot structures. We use a total Lagrangian formulation. After discretization, the degrees of freedom are the joint variables and the elastic degrees of freedom of each link. The elastic motions are referred to the rigid configuration of the considered link. The control law is obtained by using a non-linear decoupling technique which is applied to the joint variables. A second control loop performs an active damping of the elastic motions: it is based on the linearized model and uses the LQR method. This approach has been experimented with a two flexible links robot. The results demonstrate its feasibility. Further developments mainly concern theoretical aspects on the robustness of these control laws, the identification of the model parameters and the choice of other appropriate modelling techniques.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1657-1668 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1637-1655 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In multibody dynamics one may use a number of mode shapes for each body to capture flexibility effects. If a co-rotational and co-translational formulation is applied, rigid body motions are described using special generalized co-ordinates for reference frames and such motions cannot therefore be spanned by the chosen set of mode shapes.Constraint modes are attractive to use following the FEM direct stiffness appraoch and can give accurate solutions with a minimum number of mode shapes in static and low frequency excitation problems. A set of constraint modes often span rigid body motions.The objective of this paper is to show the usefulness of combining constraint modes with an orthogonalization and subsequent rigid body mode shape rejections. In this way the remaining deformation modes together with the reference frame generalized co-ordinates span the solution space of the original set of constraint modes.Two numerical examples are included. A simulation of a truck frame vehicle passing a bump was carried out. A rotating structure with positioning PID-control was studied.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1627-1648 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The boundary element method is applied to transient viscous incompressible flow. The time-domain formulation allows a boundary-only solution for linear Stokes flow. For higher speed flows in which the non-linear convective effects cannot be ignored, a volume integral must be retained. However, the introduction of reference velocities often limits the non-linear region to the vicinity of obstacles or bounding surfaces. Additionally, the volume terms are rewritten to eliminate the need for the calculation of velocity gradients. A general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis. This implementation includes a Newton-Raphson algorithm, permitting accurate solutions up to the moderate Reynolds number range. Several numerical examples are provided to validate the present approach.
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1669-1682 
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    Notes: The weak connection conditions and an independence principle for internal displacements which can guarantee the numerical stability of the incompatible element solution are presented in this paper. A number of problems such as the uncoupling of the two types of displacement functions in the λ-type element, zero energy modes, etc., have been investigated. Some simple and practical guidelines for establishing trial functions of non-compatible elements are given.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 29-43 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A refined global-local method was proposed to improve the efficiency of finite element analysis. The proposed method was based on the regular finite element method in conjunction with three basic step, i.e. the global analysis, the local analysis and the refined global analysis. In the first two steps, a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest. These local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses. In the third step, a new global displacement distribution based on the results of the previous two steps was assumed for the analysis, from which much improved solutions for both stresses and displacements were produced. Numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method. Further, this method is suitable for parallel computation.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 79-101 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Issues related to the constitutive modelling and computational treatment of strain localization are examined for the class of rate independent solids. The significance of the constitutive description in localization problems is emphasized and constitutive models currently employed are briefly reviewed. Difficulties faced in finite element analysis, fundamentally associated with the loss of ellipticity of the related boundary value problem, and present trends in the computational treatment are discussed and illustrated by numerical examples.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 45-61 
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    Notes: The paper presents results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods1 have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 63-78 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The application of the Trefftz method for calculating wave forces on offshore structures is presented. Indirect and direct formulations using complete and non-singular systems of Trefftz functions for the Helmholtz equation are posed in this paper. An effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force. The numerical examples show that the present method is highly efficient and accurate.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 149-169 
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    Notes: This paper discusses the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of the C1 deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 211-212 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 215-215 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 219-222 
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1027-1039 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational higher-order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through-thickness displacement gradients with the requirement of a least-square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simple C0- and C-1- continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two-node stretching-bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysis of deep beams.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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