Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi -material topology optimization method based on the hybrid reliability of the probability -ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design. The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads. The topology optimization formula is combined with the ordered solid isotropic material with penalization (ordered-SIMP) multi -material interpolation model. The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p -norm function. Furthermore, the sequential optimization and reliability assessment (SORA) is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization (DTO) problem. Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point (MPP). In each cycle, the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle. The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method (MMA) is used to update design variables. Finally, the validity and feasibility of the method are verified by the numerical example of L -shape beam design, T -shape structure design, steering knuckle, and 3D T-shaped beam.