Mathematical design and graphical solution of the multiple bifurcation equations of a 4-DoF benchmark model

摘要

A 4 degree-of-freedom (DoF) benchmark model of multiple bifurcation (MB) in compound stability problems of nonlinear structures is proposed. In the MB model, the governing equations are designed to be highly simplified when two critical modes exist in the singular Jacobian matrix. The resulting MB equations can be solved analytically through manual calculation. To verify the applicability, graphical solution methods are applied to solve the MB equations and visualize the multiple path branching through a graphical monitor. The proposed benchmark model and graphical strategies can help understand the stability phenomenology and MB in the stability design of large-scale finite element models.