Minimum stress optimal design with the level set method

This paper is devoted to minimum stress design in structural optimization. We propose a simple and efficient numerical algorithm for shape and topology optimization based on the level set method coupled with the topological derivative. We compute a shape derivative, as well as a topological derivative, for a stress-based objective function. Using an adjoint equation we implement a gradient algorithm for the minimization of the objective function. Several numerical examples in 2-d and 3-d are discussed.