Multi-constrained topology optimization via the topological sensitivity

The objective of this paper is to introduce and demonstrate a robust method for multi‐constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The primary advantages of the proposed method are: (1) it rests on well‐established augmented Lagrangian formulation for constrained optimization, (2) the augmented topological level‐set can be derived systematically for an arbitrary set of loads and constraints, and (3) the level‐set can be updated efficiently. The method is illustrated through numerical experiments.