Discontinuity in sensitivity of elastoplastic bifurcation loads of finite dimensional symmetric structures

Abstract

A detailed discussion is presented on discontinuity in elastoplastic bifurcation load factor and its design sensitivity coefficients of symmetric finite dimensional structures subjected to symmetric proportional loads. Due to the discontinuity of the design sensitivity coefficients with respect to the design variables, verification of the analytical design sensitivity coefficients by comparing with the results by a finite difference approach can show only local accuracy of the results which is not sufficient if the method of design sensitivity analysis is applied to optimum design problems. It is shown in the example of a simple column that the approach of tracing the yield points in conjunction with the interpolation technique is shown to be most effective for finding continuously varying bifurcation load factor and the design sensitivity coefficients which are valid in wide range of the design variables.