Numerical treatment of complete load-deflection curves

A method for direct computation of complete load{de ection curves, including both primary and secondary branches, as well as exact calculation of singular points is presented. The method used for path following is the cylindrical arc-length method in accordance with Cris eld.1 To calculate singular points, an extended system, as proposed by Keener and Keller,2 has been adopted. The numerical problems arising from ill- conditioned sti ness matrices near the singular points, are circumvented using a de ation technique. By a modi cation of the constraint equation used in the arc-length method, a reliable method for branch switching has been obtained. This leads to a uni ed approach to complete path following of structures with limit and bifurcation points. The use of this approach is demonstrated both on a simple two-bar truss as well as on a star-shaped shallow truss dome which exhibits complex stability characteristics. Comparisons are made with calculations found in the literature.