A METAHEURISTIC FRAMEWORK TO IMPROVE NONLINEAR FINITE ELEMENT ANALYSIS

Most industrial-practical projects deal with nonlinearity phenomena. Therefore, it is vital to implement a nonlinear method to analyze their behavior. The Finite Element Method (FEM) is one of the most powerful and popular numerical methods for either linear or nonlinear analysis. Although this method is absolutely robust, it suffers from some drawbacks. One of them is convergency issues, especially in large deformation problems. Prevalent iterative methods such as the Newton-Raphson algorithm and its various modified versions cannot converge in certain problems including some cases such as snap-back or through-back. There are some appropriate methods to overcome this issue such as the arc-length method. However, these methods are difficult to implement. In this paper, a computational framework is presented based on meta-heuristic algorithms to improve nonlinear finite element analysis, especially in large deformation problems. The proposed method is verified via different benchmark problems solved by commercial software. Finally, the robustness of the proposed algorithm is discussed compared to the classic methods.

Keywords:

Nonlinear analysis , finite element method , meta-heuristic algorithm , continuum mechanics , enriched firefly algorithm , large deformation , optimization.