NUMERICAL TREATMENT OF COMPLETE LOAD-DEFLECTION CURVES

A method for direct computation of complete load-deflection curves, in cluding both primary and secondary branches, as well as exact calculat ion of singular points is presented. The method used for path followin g is the cylindrical arc-length method in accordance with Crisfield.(1 ) To calculate singular points, an extended system, as proposed by Kee ner and Keller,(2) has been adopted. The numerical problems arising fr om ill-conditioned stiffness matrices near the singular points, are ci rcumvented using a deflation technique. By a modification of the const raint equation used in the arc-length method, a reliable method for br anch switching has been obtained. This leads to a unified approach to complete path following of structures with limit and bifurcation point s. The use of this approach is demonstrated both on a simple two-bar t russ as well as on a star-shaped shallow truss dome which exhibits com plex stability characteristics. Comparisons are made with calculations found in the literature. (C) 1998 John Wiley & Sons, Ltd.