Development of a Sensitivity Analysis Method in Prostbuckling Problems.

Abstract

An analysis method to evaluate the sensitivities in postbuckling problems is developed. In recent years, sensitivity analysis using the perturbation method has been applied to nonlinear static/dynamic problems. In postbuckling analysis, however, the load values at limit or bifurcation points are also unknown variables of which the gradients cannot be evaluated by the conventional sensitivity analysis. The new extended formulation can calculate the gradients of the load values as well as the displacement gradients under a constant 'arc-length' condition, which is generally used as a path-following method to find the equilibrium state beyond the limit or bifurcation points. A couple of buckling analyses of sheli structures are demonstrated to examine the validity of this method, and satisfactory results are obtained.