VELOCITY FIELD LEVEL SET-BASED ROBUST TOPOLOGY OPTIMIZATION FOR STRUCTURAL STRESS MINIMIZATION

To address the issue that traditional deterministic topology optimization methods may lead to stress concentration-sensitive structures under load uncertainties, this paper proposes a robust topology optimization method (RTO) for structural stress minimization based on a velocity field level set framework. First, the P-norm function is adopted to globally measure the maximum stress in the structure. Then, a surrogate model for the stochastic response of the maximum stress under uncertain loads is constructed using the polynomial chaos expansion (PCE) method. The mean and standard deviation of the maximum stress are analytically derived directly from the PCE coefficients, and a robust topology optimization model is established with the objective of minimizing the linear combination of these two statistical moments, thereby balancing both the average performance and the fluctuation of stress behavior. During the optimization process, the velocity field level set method is employed to describe the evolution of structural boundaries. By combining the direct differentiation method and the adjoint variable method, analytical sensitivities of the statistical moments of the global maximum stress with respect to the velocity design variables are derived, providing accurate gradient information for topological evolution. The globally convergent method of moving asymptotes (GCMMA) is introduced to efficiently update the design variables. To verify the effectiveness and stability of the proposed method, two typical numerical examples are systematically simulated and analyzed, with comparison results validated by Monte Carlo simulation (MCS). Furthermore, the influences of weighting coefficients, load variation coefficients, and volume constraint limits on the final configurations and stress performance are investigated.