Novel methodology of Non-probabilistic Reliability-based Topology Optimization (NRBTO) for multi-material layout design via interval and convex mixed uncertainties

Abstract This paper proposes an efficient topology optimization strategy for seeking the optimal layout of multi-material structures with mixed uncertainties of interval and convexity. In conjunction with the safety criterion for local displacement and the extended power-law interpolation scheme for the material property, the task of the optimization problem is formulated as to minimize the total volume of different materials while satisfying reliability requirement. By introducing the set-theoretical convex method, uncertainty quantification analysis under mixture of interval and convex uncertainties is firstly conducted for exploring boundary rules of considered responses. Combined with the area-ratio principle and the shortest distance judgment, a novel reliability index with favorable mathematical characteristics is then defined. Moreover, for guarantee the computational efficiency as well as the iterative convergence, the adjoint-variable model is also established and the investigated minimization issue can be solved by a gradient-based optimization algorithm. Eventually, several numerical applications are given to demonstrate the validity and reasonability of the present topology optimization methodology.