Computational Strategies for Tracing Post-Limit-Point Paths with Pure Iterative Methods

Abstract

In this work alternative methodologies are proposed for following post-buckling paths without the need for a complete factorization of the stiffness matrix or any factorization at all. This is achieved with two different approaches. The first employs nonlinear versions of preconditioned conjugate-like methods and the so called conjugate and secant-Newton methods have been tested. The second approach is based on the classical Newton-Raphson or modified Newton-Raphson methods, while for the linearized problem in each iteration the preconditioned Lanczos method is employed. Both methodologies combine the convergence properties of Newton-like methods and the low storage requirements of pure iterative methods by varying the storage demands for the preconditioning matrix according to the available computer storage facilities.