Topological derivative-based topology optimization of structures subject to self-weight loading

Topology optimization of structures subject to self-weight loading has received considerable attention in the last decades. However, by using standard formulations based on compliance minimization under volume constraint, several difficulties arise once the self-weight of the structure becomes dominant, including non-monotonic behavior of the compliance, possible unconstrained character of the optimum, and parasitic effects for low densities when using density-based methods. In order to overcome such difficulties, a regularized formulation that allows for imposing any feasible volume constraint is proposed. The standard formulation based on compliance minimization under volume constraint is recovered when the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method leading to a 0-1 topology design algorithm, which seems to be crucial when the self-weight loading is dominant. Finally, several numerical experiments are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading.