High-resolution non-gradient topology optimization

Abstract Non-gradient topology optimization aims to utilize soft computing approaches to approxi-mate the optimal material distribution inside a predefined design domain of a structure. Although these approaches have the advantage of solving problems without a need for calculating gradients or sensitivities, they are associated with the drawback of coarse meshing or a limitation over the design domain. In this paper, we demonstrate how the derivative-free level-set method can eliminate this drawback without scarifying the quality of obtained topologies. We solved three benchmark numerical experiments at different levels of fine meshing. Additionally, the topological attainability is explored using image processing and models of physical problems of structural compliance, heat transfer and composite structures. The obtained results were compared to those by gradient methods. The results indicate that the proposed derivative-free level-set method can make the number of decision variables independent of the meshing level, but the level of attainable topological features. They demonstrate that the proposed approach can attain complex topological details using small numbers of decision variables at relatively low computational costs.