A critical displacement approach for predicting structural instability

Published in Comput. Methods Appl. Mech. Engrg., Vol. 134 (1-2), pp. 135-161, 1996
doi: 10.1016/0045-7825(96)01032-8

Abstract

A new technique for predicting structural instability points using the finite element method is presented. The approach is based on the estimation of the critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this procedure are given together with explicit forms of the secant stiffness matrix for finite element analysis of solids and trusses. The accuracy and effectiveness of the method are clearly shown in a number of examples of two- and three-dimensional bar structures.