A Topological Optimization Method Considering Stress Constraints

Abstract

Sizing and shape structural optimization problems are normally stated in terms of a minimum weight approach with constraints that limit the maximum allowable stresses and displacements. However, topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach. In this kind of formulations, while no stress or displacement constraints are taken into account. Moreover in some FEM minimum weight topology optimization method with stress constraints formulation, transferred stress constraint functions cannot completely embody stress constraint requirements. In this paper, we build an equivalent optimization model for the topological optimization problem with the objective function being the structural weight and only stress constraints. In this model all element stress constraints of the structure being optimized under a load case are replaced by its most potential active stress constraint and average stress constraint. In order to make the stress constraint approximations hold true during an optimization process, we propose a solving strategy of varying stress limits. And a set of stress sensitivity formulation is derived and a new topology optimization method is developed and implemented. Several simulation examples show that stress sensitivity computation cost may be greatly reduced and there is not any objective oscillation phenomenon, and verify that the proposed method is of validity and effectiveness.