Reliability-based topology optimization using LRPIM surrogate model considering local stress and displacement constraints

Abstract

This paper presents a novel decoupled framework for reliability-based topology optimization (RBTO) that aims to find optimal material configurations while meeting local stiffness and strength constraints. To effectively address the nonlinear displacement and stress reliability constraints, the proposed framework replaces the conventional first-order reliability method (FORM) with the more accurate Local Radial Point Interpolation Method (LRPIM). This substitution overcomes the limitations of FORM in approximating high-dimensional nonlinear problems. The framework includes the qp-relaxation criterion and a global stress aggregation technique to avoid stress singularities. For multi-constrained optimization, the adjoint vector method is used for design sensitivity analysis, followed by a gradient-based algorithm to solve the structural optimization problem. Numerical examples are presented to validate the effectiveness of the proposed RBTO methodology, demonstrating its superiority in both accuracy and reliability compared to the Sequential Optimization and Reliability Assessment (SORA) method. The comparative analysis highlights the efficiency and precision of the proposed method across different reliability approaches, making it a robust tool for addressing complex engineering challenges.