Solving nonlinear structural problems by associating line-search and pathfollowing techniques.
The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Federal de Ouro Preto (UFOP) |
| Repositorio: | Repositório Institucional da UFOP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.ufop.br:123456789/19015 |
| Acceso en línea: | https://www.repositorio.ufop.br/handle/123456789/19015 https://doi.org/10.55905/revconv.17n.6-300 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlinear structural analysis Finite element method Line-search Path-following methods Newton-raphson iterations |
| Sumario: | The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence. |
|---|