Nonlinear static analysis of extreme structural behavior: Overcoming convergence issues via an unconditionally stable explicit dynamic approach

Abstract

Simulating extreme structural behavior is of vital importance as it is a major means to study the damage and failure mechanism of engineering structures. However, convergence issues frequently occur when simulating structural response under extreme loading using traditional nonlinear solution strategies, e.g., the Newton–Raphson family of methods. Though commercial finite element software provides explicit dynamic methods to overcome this issue, they are only conditionally stable and require a small time step size. In this paper, a new explicit dynamic approach to simulate static problems involving extreme structural behavior is presented. The multi-support excitation pattern is employed to apply a nodal displacement history of the problem in a dynamic way, then the unconditionally stable explicit KR-α method is used to eliminate the convergence issues. Three examples are presented to illustrate the effectiveness of the proposed dynamic approach, and a parametric study is conducted to investigate the influence of the algorithmic parameters. The results indicate that the proposed method provides the same accuracy as the traditional static method without any convergence issues.