A finite element optimization technique to determine critical imperfections of shell structures

Abstract

Geometric imperfections play a significant role in the evaluation of the buckling capacity of thin-walled structures. Since the pattern and distribution of such imperfections take a random variation, the determination of a critical imperfect shape that leads to the minimum buckling load becomes a challenge. In this study, an optimization technique based on binary coded genetic algorithms is used together with a nonlinear finite element model to identify the critical imperfection pattern for thin-walled welded structures. The finite element model is based on a consistent sub-parametric shell element that accounts for the effect of both geometric and material nonlinearities. The binary coded genetic algorithm is used as the optimization means to arrive at the imperfection pattern leading to the near globally minimum buckling load. A previously developed mathematical model is employed to describe the imperfection bulges associated with lines of weldment. The method is demonstrated by considering the nonlinear stability analysis of both a circular cylinder subjected to pure axial compressive load and a conical tank under hydrostatic pressure. The combined genetic algorithm – finite element code is used to determine the critical imperfection bulge patterns for the two problems, as well as their associated buckling loads.