Non-probabilistic reliability based topology optimization design of two-material structures

Using the convex model description and the quantified definition of the non-probabilistic reliability, topology optimization of two-material structures considering uncertainties in material properties, geometry and loads is studied. Based on the extended penalization scheme of relative density, a continuous minimax optimization problem, which satisfies the material volume constraint and the reliability requirement, is presented for finding the united distribution of two candidate materials. The minimax problem is solved in the sequential approximate programming manner by embedding a direct iterative formula and the method of moving asymptotes (MMA). The computation cost is thus greatly decreased since the original problem is transformed into a series of deterministic ones. Numerical examples show that system uncertainties may have considerable effects on the optimal united layout of two-material structures. The results prove that a powerful approach for the topology design of two-material structures is furnished by the proposed numerical technique.