Optimization of thin-walled structures with geometric nonlinearity for maximum critical buckling load using optimality criteria

In this study, two optimality criteria are presented for shape optimization of thin-walled structures with geometric nonlinearity modeled by finite elements. The optimization problem considers the thickness and geometry design variables, and aims to maximize the critical load of the structure subject to constant total mass. Results of the optimization with optimality criteria are compared with those found by the gradient-based sequential quadratic programming method. It is shown that the optimum shape can be found using this method without performing the sensitivity analysis, and in less number of iterations compared to the standard gradient-based methods of optimization.