Stress-constrained topology optimization of heterogeneous lattice structures for additive manufacturing

Abstract

This study presents a topology optimization method for heterogeneous lattice structures subject to stress constraints. The proposed approach extends the ordered SIMP (Solid Isotropic Material with Penalization) framework to incorporate a composite material failure criterion. Specifically, a modified Tsai–Hill yield criterion is employed to characterize the anisotropic yielding behavior of the heterogeneous lattice, which is subsequently integrated into the optimization as a stress constraint. To address the variation in yield strength across different lattice configurations, a normalization strategy is applied to the stress field. Additionally, a P-norm aggregation scheme is introduced to efficiently handle local stress constraints while reducing computational cost. The equivalent elastic tensor and yield strength of each lattice configuration are obtained using a representative volume element (RVE) based on homogenization theory. The effectiveness of the proposed method is demonstrated through a series of 2D cases, achieving lightweight structural designs that satisfy stress constraints. Finally, full-scale mechanical analysis and 3D printing experimental validation further confirm the strength reinforcement of the optimized results.