Topology optimization with stress constraints: Reduction of stress concentration in functionally graded structures

This presentation describes a topology optimization framework to design the material distribution of functionally graded structures with a tailored Von Mises stress field. The problem of interest consists in obtaining smooth continuous material fraction distribution that produces an admissible stress field. This work explores the topology optimization method for minimizing volume fraction of one of the phases considering stress constraints. Existence of inherent material microstructure requires consideration of the micro level stress field, which is computed through a mechanical concentration factor based on the local stress in each phase of the material. Thus, p-norm of the Von Mises stress in the microstructure is considered as a global constraint. To illustrate the method and discuss its essential features, we present engineering examples of axisymmetric FGM structures subjected to body forces.