This paper on "Detection of Critical Points Using Multigrid Methods" was presented at the NAFEMS World Congress on Design, Simulation & Optimisation: Reliability & Applicability of Computational Methods - 9-11 April 1997, Stuttgart, Germany.

Abstract

We describe multigrid methods for use with various continuation procedures to trace equilibrium paths and locate critical points of structures discretized using the finite element method. We also outline a reconditioning technique to remove the ill-conditioning inherent at or near a critical point. A simple two dimensional problem demonstrates the performance of the methods. We show that the multigrid method has potential for quickly examining the collapse of practical engineering structures.