A new approach for stress-based topology optimization: Internal stress penalization

In this paper, a new method is proposed for stress-based topology optimization. The basic idea is to perform compliance-based topology optimization while concurrently penalizing material in which the stress exceeds the admissible stress. Penalization of overstressed material is realized by considering it as damaged. Since damaged material will contribute less to the overall stiffness of the structure, the optimizer will promote a design with a minimal amount of damaged/overstressed material. The process of penalizing overstressed material can be regarded as analogous to the penalization of intermediate densities to obtain a black and white design, often used in topology optimization. In our problem
formulation, the admissible stress criterion is not imposed as a hard constraint. Therefore, using this method, the considered problems do not suffer from singular optima related to vanishing stress constraints. Furthermore, the computational costs are manageable since only one objective and one constraint are considered. The proposed method is verified by applying it on two test problems.