Path-following technique based on residual energy suppression for nonlinear finite element analysis

A new kind of path-following technique along with a new automatic load incrementation procedure is proposed. The path-following technique is based on the suppression of the residual energy in every iteration. The method not only offers a simpler procedure than the existing ones, but also enables one to update the stiffness matrix easily whenever necessary. A cylindrical type of constraint surface is provided to assist the method in passing through critical points. The proposed automatic load incrementation procedure utilizes a concept which is based on the geometry of the equilibrium path represented by a stiffness parameter. Both the path-following technique and the automatic load incrementation procedure show a good capability in tracing equilibrium paths with multiple loops in the example problems.