Stress-constrained topology optimization based on maximum stress measures

Abstract

This paper proposes two effective constraint schemes to address the stress-constrained topology optimization of continuum structures. By considering the maximum stress measure in the global and local forms, respectively, the STM (stability transformation method)-based stress correction scheme and the violated set enhanced stress measure are developed to tackle the challenging issues from numerous local stress constraints and highly nonlinear stress behavior. Particularly, a stress aggregation function is involved in the design sensitivity analysis. Moreover, the nodal variable based SIMP method and adjoint sensitivity analysis are employed to solve the optimum topological design problems with two different optimization formulations. Finally, several representative examples demonstrate the validity of the present approach. It is also indicated that the numerical performance of the stress aggregation function is closely related to the problem formulation of topology optimization. The STM-based stress correction scheme is appropriate to the material volume minimization design, while the violated set enhanced stress measure is suitable for the mean compliance minimization design. Meanwhile, the proposed optimization approach can handle the stress-constrained topology optimization with easy implementation, low computational cost and stable convergence.