Quantile-based sequential optimization and reliability assessment for shape and topology optimization of plane frames using L-moments

Uncertainty is inevitable in the real physical world, and it is necessary to take into account its effects on the structural design and optimization processes. In this study a reliability-based shape and topology optimization method is proposed for plane frames. The reliability constraint is expressed in terms of quantile which is estimated by using the maximum entropy method subject to constraints on the sample linear moments (L-moments) with small sample size. An iterative scheme of sequential optimization and reliability assessment is employed to solve a series of deterministic optimization problems with shifted boundaries on the constraints. Derivative of the quantile function is obtained by solving a convex optimization problem, instead of solving a system of nonlinear equations. Force density method is applied to an auxiliary truss model for simultaneous shape and topology optimization of plane frames to alleviate the difficulties caused by melting nodes. It is demonstrated by the benchmark and numerical examples that the quantile function can be appropriately estimated by the proposed method, and the solution satisfying the required reliability constraint can also be achieved.