Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

Wei Shen, Makoto Ohsaki, Makoto Yamakawa

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a worst case approach for robust geometry and topology optimization of plane frames with global stability constraint. Uncertainty is assumed to exist in the nodal locations and cross-sectional areas, and the worst values of the objective and stability constraint functions are relaxed to the quantile structural responses represented by the order statistics with given robustness and confidence levels. In order to alleviate the difficulty caused by melting nodes to some extent, the force density method is applied to an auxiliary truss model for geometry optimization of the frame, and the closely spaced nodes are merged. A method is presented for generating correlated imperfections for the nodal locations along each member, and a penalization approach is proposed for geometrical stiffness matrix to exclude superficial local buckling. It is demonstrated in the numerical examples that the result of robust optimization obtained by the proposed method is less sensitive to the uncertainty, and the stability constraint is also satisfied under uncertainty with the specified robustness and confidence levels.

Original languageEnglish
Pages (from-to)3653-3677
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Volume122
Issue number14
DOIs
Publication statusPublished - 30 Jul 2021

Keywords

  • force density method
  • order statistics
  • plane frame
  • robust optimization
  • stability constraint

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