| Advancements in mathematical tools are increasingly encouraging optimization of problems with a large number of design variables. These approaches are still constrained in terms of practical computational times, especially in the case of a nonlinear problem. A computationally efficient and effective method has been developed to solve large and complex optimization problems using a global-local method. This method tries to exploit the advantage of performing local optimization of regions using submodeling, simultaneously retaining its global nature by providing periodic updates to the local optimization conditions. Local optimization performed under perturbed conditions has shown increased robustness of the optimal design, consequently improving the convergence characteristics of the process. The approach is evaluated with a shape optimization problem of a hole in a square plate to study the effects of local model size and magnitude of variations. To understand the problem better, a beam problem is optimized using the global local approach. Crashworthiness shape optimization of an automobile energy absorber was performed with the proposed global local approach. Decomposition of this problem is achieved by using different levels of design variable discretization and problem specific methods for increased performance. The method proposed is generic in nature and has been successfully implemented in ABAQUS and LSDYNA with capabilities of being used in future studies. |
