Reliability-Based Proportional Topology Optimization of Continuum Structures with Smooth Boundaries

Abstract

This study presents a reliability-based proportional topology optimization (RPTO) framework for continuum structures, specifically designed to achieve smooth, manufacturing-ready boundaries under multi-source uncertainties. By integrating the Proportional Topology Optimization (PTO) algorithm with a Level Set Method (LSM), the approach bypasses the need for high-order sensitivity information while ensuring high-fidelity boundary representation. A hybrid decoupling strategy is employed to decompose the reliability-based topology optimization (RBTO) problem into a reliability analysis sub-problem and an equivalent deterministic topology optimization (EDTO) sub-problem. Uncertainties in geometry, material volume, and loading are characterized via a probabilistic framework using the First-Order Reliability Method (FORM). Numerical results for 2D and 3D benchmarks demonstrate that the RPTO method effectively captures the influence of the target reliability index on structural morphology, yielding robust designs that satisfy strict probabilistic constraints without the "gray areas" common in density-based methods.