A weight-reduction structural topology optimization method using a constraint-shift strategy and a body-fitted polygon mesh

Abstract

Weight-reduction structural topology optimization (TO) with stress constraints represents an intrinsically nonlinear problem. To improve solvability, relaxed stress constraints are employed to enlarge the feasible design space, enabling gradient-based optimizers to identify admissible solutions. Meanwhile, the widely used SIMP interpolation cannot avoid the intermediate densities. To ensure manufacturability, a binarization step, typically achieved by thresholding, is therefore required to convert these "gray" densities into a solid-void (1-0) design. However, the stress constraint, without relaxation, cannot be guaranteed to be satisfied on this binary design. To overcome this limitation, we propose a stress-constrained TO (SCTO) method that directly enforces non-relaxed local stress constraints. The core of the method is a constraint-shift strategy, which introduces an adaptive shifting vector to reconcile the discrepancy between relaxed and non-relaxed stresses. This formulation integrates seamlessly with standard gradient-based solvers. Furthermore, the accuracy of stress evaluation is enhanced by performing the analysis on a body-fitted polygonal mesh. Compared with uniform grid-based representations, the body-fitted polygon mesh conforms more closely to evolving boundaries. It can improve geometric fidelity in regions of stress concentration. Several benchmark 2D examples demonstrate the effectiveness of the proposed approach. The combination of constraint shifts and body-fitted polygon discretization provides a scalable pathway for SCTO in applications where local safety requirements are critical.