Topology Optimization for Static Nonlinear Structures Using Big Bang-Big Crunch Algorithm

Abstract

The purpose of this thesis is to suggest the topology optimization (TO) and topological shape optimization (TSO) methods for nonlinear static stiffness structural problems using the Big Bang-Big Crunch algorithm (BB-BC). The BB-BC is a meta-heuristic method motivated by the evolution of the universe called the Big Bang and Big Crunch Theory; the algorithm mainly operates by the idea that various substances are spread out from the initial Big Bang and are gathered again by the Big Crunch of these substances. In this thesis, in order to apply for nonlinear static stiffness structural optimization, modifications on the original BB-BC were performed to improve the performance of the method. In particular, the modification of the penalization factor has been introduced in order to prevent the localization of obtained solutions. The penalization factor causes polarization of density distribution that leads the solutions to local optimum in the case of sensitive and complicated nonlinear static stiffness structural problems. We improved the stability and robustness of the TO nonlinear static stiffness structural problems by reducing of the penalization factor. In addition, a parametric study for the parameters was performed and the performance of the existing TO and TSO methods using the BB-BC for linear structural problems significantly improved. We extended the consideration range of parameters by at least 2 times to improve existing methods. As a result of parametric study, both convergence rate and CPU time have improved by over 50%. The performance of our proposed TO and TSO methods using the BB-BC for nonlinear static stiffness problems was also improved. In the TSO method using the BB-BC, the stabilization index is introduced to prevent obtaining local optimization solutions and to improve the convergence rate. Stabilization index is the point where all the structures are connected and stabilized. After that, the search will be carried out only with the current structure without applying the previous density. To verify the effectiveness of the suggested method using the BB-BC, examples for nonlinear static stiffness structural optimization were provided to compare with the nonlinear static stiffness structural optimization method based on the ABCA. Our results demonstrate that the proposed algorithm can be successfully applied to the TO and TSO methods and the results show that structural optimization scheme using the BB-BC provides a fast convergence rate, a robust optimum design, and a stable optimization process.