Shape and topology optimization of plane frames via quantile-based sequential optimization and reliability assessment with global stability constraint

Abstract

In this paper a framework of quantile-based sequential optimization and reliability assessment (SORA) is extended to consider the global stability constraint in the optimization of plane frames. Uncertainty is considered on the structural side without any prior assumptions on their distribution information, and two novel stopping criteria with a reduction coefficient are employed to smoothly shift the constraint boundary for the next iteration. Force density method is introduced for the shape optimization of plane frames to avoid the existence of the melting nodes, and the geometrical stiffness matrix is also penalized to exclude pseudo local buckling modes. The numerical examples illustrate that with the help of reduction coefficients, the shifts of different constraint boundaries in SORA become smoother and the convergence of sequential optimization is improved, and due to shape optimization, the reliability of structural stability can be satisfied with limited increase of structural volume of the one without considering stability. Moreover, it is also shown in the cantilever beam and bridge examples that global structural stability can be enhanced by applying nodal displacement constraints with higher reliability.

Graphical abstract

Keywords

quantile function / sample L-moment / sequential optimization and reliability assessment / force density method / stability constraint / maximum entropy method

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The Author(s). This article is published with open access at link.springer.com and journal.hep.com.cn