Post-buckling analysis of nonfrictional contact problems using linear complementarity formulation

Abstract

A linear complementary problem formulation is proposed for post-buckling analysis of geometrically nonlinear structures with nonfrictional contact constraints. The arc-length method with updated normal plane constraint used to trace the equilibrium paths of the structures is combined to generate a path-following algorithm as a predictor-corrector procedure. The initial load increment is determined in the predictor phase, considering the change of contact status. For the corrector phase, the unknown load scale parameter is eliminated using the arc-length constraint. The unknown contact variables such as contact status and contact forces can be directly solved by the linear complementarity problem without any ad-hoc technique. Several newly defined buckling and post-buckling with contact constraints are solved to illustrate the algorithm and the detail complex behaviors. It is demonstrated that the algorithm is very stable and efficient in dealing with the rather difficult class of buckling problems with obstacles.