A null space algorithm for solving multiple-constrained topology optimization problems with topological derivatives

Abstract Topology optimization is widely regarded as one of the most effective techniques for structural design. However, current algorithms used for level-set approaches often introduce fine tuning of parameters and generally exhibit low speed of convergence, specially when dealing with multiple constraints. Consequently, a fundamental aspect in topology optimization is to have access to a robust optimization scheme. Recently, the null space algorithm has exhibit solid performance when considering density and shape optimization approaches. The aim of this paper is to extend the null space approach to also consider topological derivatives for level-set methods. The idea relies on continuing the current fix-point techniques with the null space algorithm. The proposed optimizer has much less free parameters in comparison with the well-known augmented Lagrangian algorithm. Besides, we also consider box constraints in the dual computation to reduce the oscillations in the density case. The proposed method naturally handles inactive constraints, which are particularly relevant for engineering applications. Several numerical examples, including multiple constraints, show that results are obtained effectively with an adequate numerical stability.