Topological derivative-based multi-material structural optimization with adaptive mesh refinement

Resumo

Topology optimization of structures has been a topic great interest and intense research in the last decades. In simple terms, topology optimization aims at finding a material distribution within a given design domain which minimizes a shape functional. Typically, most works in this area mainly focus on considering the problem of obtaining optimal topologies composed of a single material. However, recent efforts and developments allowed for the incorporation of more than one material in the optimization problem. More specifically, we adopt here a topology optimization algorithm based on the topological derivative together with a domain representation on a fixed mesh with the help of multiple level-set functions. The topological derivative measures the sensitivity
of a given shape functional with respect to an infinitesimal singular domain perturbation, such as holes, inclusions, source terms or cracks. In this work, the topological derivative is used in the optimization procedure as a steepest descent direction, like in any method based on the gradient of the cost functional. In addition, adaptive mesh refinement procedures are performed as a part of the optimization scheme for an enhanced boundary resolution of the final topology. Finally, numerical experiments of classical benchmarks in structural optimization are performed into two and three spaces dimensions to show the effectiveness of the proposed approach.