A compliance-based topology optimization approach using conservative convex separable approximations and PSB Hessian estimation

Resumo

In topology optimization, methodologies for updating design variables, such as the widely-used Optimality Criteria (OC), play a pivotal role in efficiently addressing problems with monotonically decreasing objectives subject to certain design constraints. However, despite its effectiveness, the OC method is derived from first-order optimality conditions. These conditions may not fully capture the nuances of more complex optimization problems, potentially leading to suboptimal or inefficient solutions. In this work, we use conservative convex separable approximations (CCSA) of the objective function, alongside with a PSB method for estimating the diagonal terms of the Hessian matrix. Three variations are considered: quadratic, logarithmic, and square-root approximations. This approach aims to enhance the efficiency and effectiveness of objective minimization in topology optimization problems subject to a volume constraint. To demonstrate the efficacy of the aforementioned methodology, several case studies are presented and evaluated using both the OC method and the CCSA update scheme. The obtained results and performance metrics are compared, providing clear evidence of the advantages offered by the proposed approach.