Branch Switching in Bifurcation of Structures

Abstract

A branch‐switching strategy in an elastostatic bifurcation problem is described. Only linearized incremental equations are used. Higher‐order terms of increments and eigenvalue analysis are not required. Uneconomical iteration during random access to the secondary path can be avoided. Near the bifurcation point, the loading parameter is fixed to define a constant‐loading plane that intersects the equilibrium branches. All these intersections are stationary points of potential energy located closely in the vicinity of bifurcation point. A trajectory passing through these intersections is introduced at the assumed loading level. Line search with a termination criterion will be initiated to detect a stationary point of potential energy in the tangent direction of the curve. Iteration is then started from this detected stationary point to attain a regular point on the postbifurcation path. In a complex branching situation, line search in the improved tangent direction or tracing of the trajectory is recommend...