Pinpointing Bifurcation Points and Branch-Switching

Abstract

Bifurcation points require a special treatment in computational stability analysis of nonlinear structures. Tracing of the nonlinear equilibrium response, pinpointing of stability points and branch-switching are the foremost necessary procedures for bifurcation problems. The primary concern of this paper is to review the methodology, including all of these fundamental strategies for nonlinear bifurcation analysis. The underlying ideas in the background of the strategies are locally and globally convergent nonlinear solution methods. The global pinpointing procedures are recent contributions in the present paper, too. As the optional global paths to the target singular point, bypass, and homotopy path are introduced. The starting point, at which the global pinpointing will be initiated, may be an arbitrary equilibrium or nonequilibrium point. Regarding branch-switching, the homogeneous and particular solutions of singular stiffness equations are computed to predict the branching direction. Hilltop branching receives a special attention. Numerical examples including simple, multiple, and hilltop branching are presented.