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  • 1
    Electronic Resource
    Electronic Resource
    ON THE SIGN OF THE DETERMINANT OF THE STRUCTURAL STIFFNESS MATRIX FOR DETERMINATION OF LOADING INCREMENT IN ARC-LENGTH ALGORITHMS (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 47-49 
    Details
    ISSN: 1069-8299
    Keywords: nonlinear structural analysis ; arc-length algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we have proved in theory that the sign of the current stiffness matrix provides a correct indicator for determining the sign of the loading parameter in the arc-length algorithm before the first bifurcation point is encountered, but may not be the case thereafter. © 1997 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    ITERATIVE SOLUTION OF COUPLED FE/BE DISCRETIZATIONS FOR PLATE-FOUNDATION INTERACTION PROBLEMS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1889-1901 
    Details
    ISSN: 0029-5981
    Keywords: coupled finite element boundary element analysis ; iterative solution ; plate-foundation interaction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate-foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2209-2229 
    Details
    ISSN: 0029-5981
    Keywords: eigenvalue problem ; conjugate gradient method ; Rayleigh quotient ; asymptotic analysis ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is shown that with a generally selected preconditioning matrix the actual performance of the PCG scheme may not be superior to an accelerated inverse power method. Finally, some test problems in the finite element simulation of 2-D and 3-D large scale structural models with up to 20200 unknowns are performed to examine and demonstrate the performances.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    A multi-grid enhanced GMRES algorithm for elasto-plastic problems (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 1441-1462 
    Details
    ISSN: 0029-5981
    Keywords: GMRES ; Galerkin multi-grid ; variable preconditioning scheme ; conjugate gradient method ; large-scale elasto-plastic problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A combination of both GMRES and multi-grid (MG) methods is presented in this paper for solving large-scale two- and three-dimensional elasto-plastic problems, in which each MG iteration cycle serves as the preconditioning step for the GMRES procedure. A particular multi-grid approach, termed the Galerkin multi-grid scheme, is considered and the main effort is devoted to the implementation aspects of the proposed algorithm. Numerical examples, characterised by large-scale (up to 82145 DOF), strong non-linearity (nearly plastic limit state, necking and localization) and severe ill-conditioned states (presence of loading limit points), and also involving symmetric and unsymmetric as well as SPD and indefinite system matrices, are provided. The numerical results illustrate that the proposed method exhibits a remarkable performance in terms of efficiency and robustness in all circumstances. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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