Branch Switching for Pitchfork Bifurcation in Nonlinear Finite Element Method

摘要

A general branch-switching approach is proposed, based on pseudo arc-length continuation in the nonlinear finite element method (FEM), to trace the branch solution curve at the pitchfork bifurcation point in parameter space. By this approach, branch direction can be determined without derivatives of tangent stiffness matrix. This approach is proved mathematically and is inserted into a general FEM code. Stability of equilibrium corresponding to each solution curve is estimated by the Lagrange-Dirichlet criteria. As an example, the whole process of the elastic mode jumping for rectangular thin plates, in which there are many pitchfork bifurcations in parameter space in loading and unloading, is simulated by the improved FEM code.The numerical results are identical with that of an experiment done by previous researchers.