Computing critical points and secondary paths in nonlinear structural stability analysis by the finite element method

Abstract

Stability analysis is a crucial aspect of structural design, particularly for beam, plate and shell type structures. The stability of a structure is often governed by singular points in its equilibrium path. These points usually pose serious problems to ordinary finite element solution methods and require special treatment. In this paper, the state-of-the-art of finite element path-following techniques is critically reviewed with special attention to bracketing procedures for the singular points and branch switching algorithms. Some practical aspects involved will be explained in detail and demonstrated through numerical examples at the end.