Stress-based topology optimization using an isoparametric level set method

Abstract

This paper presents a novel framework for evaluating the shape sensitivities of the von Mises stress function using an isoparametric finite-element formulation. The use of the isoparametric formulation allows us to apply the level set method to structures that are confined to irregularly shaped domains and therefore must be modeled using body-fitted, nonuniform finite element meshes. The shape sensitivities of the von Mises stress function are evaluated on this nonuniform mesh and mapped isoparametrically to a uniform Cartesian grid on which the Hamilton–Jacobi equation is solved. The paper also introduces a new approach to the enforcement of volume constraints based on the augmented Lagrangian formulation. The method is demonstrated on a series of two-dimensional problems including an isoparametric variation of the classic L-bracket problem. We show that the isoparametric level set method produces converged, feasible designs whose performance is comparable to SIMP results in terms of their final objective value.