Path following and critical points for contact problems

This work is concerned with the problem of tracing the equilibrium path in large displacement frictionless contact problems. Conditions for the detection of critical points along the equilibrium path are also given. By writing the problem as a system of non-linear B-differentiable functions, the non-differentiability due to the presence of the unilateral contact constraints is overcome. The path-following algorithm is given as a predictor-corrector method, where the corrector part is performed using Newton's method for B-differentiable functions. A new type of displacement constraints are introduced where the constraining displacement node may change during the corrector iterations. Furthermore it is shown that, in addition to the usual bifurcation and limit points, bifurcation is possible or the equilibrium path may have reached an end point even if the stiffness matrix is non-singular.