Postbuckling analysis stabilized by penalty springs and intermediate corrections

Abstract

Whenever a critical point in a non-linear finite element analysis is reached, an implicit Newton procedure is prevented from proceeding until the stiffness matrix is stabilized. Most stabilization procedures result in a damped Newton scheme. This can cause a reduced convergence rate. Based on documented stabilization strategies, an iterative procedure to reduce negative impact on the convergence rate resulting from the damping is to be proposed here. This will be done by a corrector iteration carried out between two successive equilibrium iterative steps. The equilibrium iteration is a Newton–Raphson scheme. Since the stiffness matrix has already been factorized within the preceding standard equilibrium iterative step, the stiffness matrix will be held constant during the corrector iteration, which in turn allows for a computational efficient treatment of the additional iterations. The proposed procedure has been strongly driven by Wright and Gaylord’s (ASCE J. Struct. Div., 94, 1143–1163, 1968) investigation.