Maximal stiffness design of two-material structures by topology optimization with nonprobabilistic reliability

Based on the multi-ellipsoid convex model and the quantified measure of the nonprobabilistic reliability, topology optimization of two-material structures in the presence of parameter uncertainties is investigated. The task of the optimal design problem is to distribute a given amount of two candidate materials into the design domain for acquiring the maximal stiffness while satisfying the reliability requirement. The extended power-law interpolation scheme for material properties is employed for relaxing the two-material topological design problem into a continuous-valued optimization problem. In addition, through transforming the minimax-type optimization problem into a series of deterministic ones by using a sequential approximate programming strategy, this paper aims to make the optimization design numerically tractable. The resulting mathematical programming problems are then efficiently solved by the association of the method of moving asymptotes with a heuristic iterative manner. Numerical investigations reveal that system uncertainties may have considerable effects on the optimal material layout of twomaterial structures. The proposed topology optimization methodology could yield a more reasonable two-material structural design than the conventional deterministic counterpart when the same reliability requirements need to be achieved.