A numerical approach on bifurcation in non-linear fem

In this paper, a general branch-switching approach is proposed to trace new branch solution at pitch-fork bifurcation point. The new branch direction in parameter space can be determined without the information of derivatives of tangential stiffness matrix. This approach has been inserted into a general finite element code. Stability of equilibrium corresponding to each solution is judged numerically by Lagrange-Dirichlet theorem. As an example, the whole process of mode jumping in square plates during loading and unloading is simulated by the improved finite element code. The numerical results agree with experiments done by previous researchers.