A unified multiscale framework for stress-Based topology optimization using local constraint enforcement

Abstract

This study presents a robust multiscale formulation for stress-constrained topology optimization aimed at designing lightweight and structurally resilient components. Unlike classical compliance-based methods, which may result in topologies unable to support applied loads, the proposed approach minimizes structural volume while rigorously enforcing local stress constraints. A dual-scale framework integrates macro-structural optimization with periodic micro-structural design, leveraging the Solid Isotropic Material with Penalization (SIMP) method; though it remains adaptable to other established topology optimization techniques. To address the computational challenges arising from numerous local stress constraints, we implement an Augmented Lagrangian strategy combined with polynomial vanishing constraints, eliminating the need for aggregation functions such as the p-norm or Kreisselmeier-Steinhauser functions. The resulting optimization algorithm is accurate and scalable, supported by a detailed sensitivity analysis and adjoint-based gradient computation. Numerical experiments in two dimensions validate the effectiveness of the method, demonstrating superior stress distribution and structural efficiency compared to classical formulations. This work contributes a comprehensive and scalable methodology for multiscale topology optimization under stress constraints, suitable for high-performance engineering applications.