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Method based on dual-quadratic programming for frame structural optimization with large scale

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Abstract

The optimality criteria (OC) method and mathematical programming (MP) were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.

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Authors and Affiliations

  1. Laboratory Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing, 100022, P. R. China

    Sui Yun-kang  (隋允康) (Professor, Doctor) & Du Jia-zheng  (杜家政)

  2. Laboratory Mechanics, Materials & Structures, University of Reims Champagne-Ardenne, Reims, BP1039, 51687, France

    Guo Ying-qiao  (郭英乔)

Authors
  1. Sui Yun-kang  (隋允康)
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  2. Du Jia-zheng  (杜家政)
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  3. Guo Ying-qiao  (郭英乔)
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Corresponding author

Correspondence to Sui Yun-kang  (隋允康).

Additional information

Communicated by ZHONG Wan-xie

Project supported by the National Natural Science Foundation of China(No.10472003); the Natural Science Foundation of Beijing(No.3002002); the Science Foundation of Beijing Municipal Commission of Education(No.KM200410005019)

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Sui, Yk., Du, Jz. & Guo, Yq. Method based on dual-quadratic programming for frame structural optimization with large scale. Appl Math Mech 27, 383–391 (2006). https://doi.org/10.1007/s10483-006-0315-z

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  • DOI: https://doi.org/10.1007/s10483-006-0315-z

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Chinese Library Classification

2000 Mathematics Subject Classification

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