Non-probabilistic reliability-based multi-material topology optimization with stress constraint

This article aims to develop a novel approach to non-probabilistic reliability-based multi-material topology optimization with stress constraints to address the optimization design problem considering external loading uncertainties. To be specific, the ordered solid isotropic material with penalization multi-material interpolation model is introduced into the non-probabilistic reliability-based topology optimization considering structural volume minimization under stress constraints, the multidimensional ellipsoidal model describes the non-probabilistic uncertainty. By utilizing the first-order reliability method, the failure probability can be estimated, and a non-probabilistic reliability index can be obtained. The global maximum stress is measured by adopting the normalized p-norm function method in combination with relaxation stress. The sensitivity analysis of the stress constraints is derived by the adjoint variable method, and the method of moving asymptote is employed to solve the design variables. Through several numerical examples, the effectiveness and feasibility of the presented method are verified to consider multi-material topology optimization with stress constraints in the absence of accurate probability distribution information of uncertain variables.