Post-buckling analysis with frictional contacts combining complementarity relations and an arc-length method

Abstract

A linear complementarity problem formulation combined with an are-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The are-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints.