An Iterative Topology Optimization Algorithm That Considers Randomness in Design Parameters

Abstract

Topology optimization often incorporates a reliability analysis to take the randomness in the design parameters into account. This strategy is inherently a double-loop procedure due to the probabilistic constraints in optimization. To simplify the calculation procedure, an equivalent-deterministic constraint, which is constructed by adding a penalty on the right hand side (RHS) of a limit state function, is used to reformulate a reliability-based topology optimization (RBTO) problem into a deterministic topology optimization (DTO) problem. To obtain a converged solution, the DTO and the search of equivalent-deterministic constraints must be executed iteratively. The accuracy and efficiency of the proposed approach are investigated through several numerical examples. Results indicated that the proposed algorithm is able to deliver an optimal topology with predefined reliability. Furthermore, one can incorporate the proposed algorithm with existing software to facilitate the design process.