Comparison of modified Riks/Wempner and homotopy methods

Abstract

A structured program has been developed to track the equilibrium path of geometrically nonlinear space structures by the modified Riks/Wempner method. The sparse normal flow code in 'HOMP ACK' is used for tracking the equilibrium paths by the homotopy method. Two subroutines were written as required by HOMPACK.

Four different structures were analyzed by these two programs. Comparison of the two methods has been carried out based on the number of Jacobian matrix evaluations and the CPU time used by the programs.

The Riks/Wempner program successfully traced the equilibrium path through the limit points and bifurcation points for all the four structures analyzed while the homotopy program could not trace the complete path for two of the structures. It has been concluded that the sparse normal flow code of HOMPACK needs to be modified.