No abstract

No abstract

No abstract

A stable Reliability-Based Design Optimization (RBDO) algorithm is proposed to produce an optimal design with a desired reliability. The main idea behind the proposed approach is to use a set of deterministic variables, called auxiliary design points, to replace the random parameters. Thus, the reliability analysis in the inner loop of an RBDO problem is relaxed. The auxiliary design points are found through an optimization procedure. The auxiliary design points are updated using the sums of the auxiliary design points and the differences between the mean values of the “pseudo” and actual random parameters in the previous step. The auxiliary design points can force the iteration of deterministic optimization to the vicinity of the probabilistic boundary. Note that in the proposed method, the coupled reliability analysis and deterministic optimization are decomposed to form a weakly coupled system. The stability and accuracy of the proposed method were investigated through linear and nonlinear numerical problems.

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.