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

• Published in: Structural safety 2022-01, Vol.94, p.102153, Article 102153
• Main Authors: Shen, Wei, Ohsaki, Makoto, Yamakawa, Makoto
• Format: Article
• Language: English
• Subjects: Convexity; Design optimization; Entropy; Force density method; Frames; Iterative methods; Maximum entropy; Maximum entropy method; Nonlinear equations; Optimization; Quantile function; Reliability analysis; Sample L-moment; Sequential optimization and reliability assessment; Shape and topology optimization; Structural design; Structural engineering; Topology; Topology optimization
• ISSN: 0167-4730; 1879-3355
• DOI: 10.1016/j.strusafe.2021.102153

•A reliability-based shape and topology optimization of plane frames is proposed.•Force density method (FDM) is incorporated to alleviate the difficulty caused by melting nodes.•Sample L-moments are used in maximum entropy method (MEM) for estimation of quantile response.•An unconstrained convex optimization problem is solved to obtained Lagrangian multipliers in MEM. 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..