Journal article
A remark on the application of the Newton-Raphson method in non-linear finite element analysis
Publication Details
Authors: | Hartmann, S. |
Publication year: | 2005 |
Journal: | Computational Mechanics |
Pages range : | 100-116 |
Volume number: | 36 |
ISSN: | 0178-7675 |
DOI-Link der Erstveröffentlichung: |
Abstract
Usually the notion "Newton-Raphson method" is used in the context of non-linear finite element analysis based on quasi-static problems in solid mechanics. It is pointed out that this is only true in the case of non-linear elasticity. In the case of constitutive equations of evolutionary-type, like in viscoelasticity, viscoplasticity or elastoplasticity, the "Multilevel-Newton algorithm" is usually applied yielding the notions of global and local level (iteration), as well as the consistent tangent operator. In this paper, we investigate the effects of a consistent application of the classical Newton-Raphson method in connection with the finite element method, and compare it with the classical Multilevel-Newton algorithm. Furthermore, an improved version of the Multilevel-Newton method is applied.
Usually the notion "Newton-Raphson method" is used in the context of non-linear finite element analysis based on quasi-static problems in solid mechanics. It is pointed out that this is only true in the case of non-linear elasticity. In the case of constitutive equations of evolutionary-type, like in viscoelasticity, viscoplasticity or elastoplasticity, the "Multilevel-Newton algorithm" is usually applied yielding the notions of global and local level (iteration), as well as the consistent tangent operator. In this paper, we investigate the effects of a consistent application of the classical Newton-Raphson method in connection with the finite element method, and compare it with the classical Multilevel-Newton algorithm. Furthermore, an improved version of the Multilevel-Newton method is applied.
Projects
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