基于对偶二次规划的大型框架结构优化方法

隋允康; 杜家政; 郭英乔

基于对偶二次规划的大型框架结构优化方法

北京工业大学工程数值模拟中心,北京 100022;2.兰斯大学 GMMS实验室,兰斯 1BP1039,51687,法国

基金项目: 国家自然科学基金资助项目(10472003);北京市自然科学基金资助项目(3042002);北京市教委资助项目(KM200410005019)

详细信息

作者简介:
隋允康(1943- ),男,辽宁大连人,教授,博导生导师(联系人.Tel:+86-10-67392239;Fax:+86-10-67392399;E-mail:ysui@bjut.edu.cn).

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- 文章访问数: 2535
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- 被引次数: 0
出版历程
- 收稿日期: 2004-04-20
- 修回日期: 2005-11-23
- 刊出日期: 2006-03-15

Method Based on Dual-Quadratic Programming for Frame Structural Optimization With Large Scale

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

摘要

摘要: 将准则法和数学规划相结合，对于不同的约束采用不同的处理方法：应力约束作为局部性约束，用0阶近似进行处理，借助满应力准则将其转化为动态尺寸下限；位移约束作为全局性约束，根据单位虚载荷法将其显式化，从而建立了满足应力和位移约束的框架结构截面优化的显式模型．为了提高模型的求解效率，根据对偶理论将大规模的框架结构优化问题转化为仅仅几个对偶变量的对偶问题，采用二次规划方法求解，算例证明该方法能极大的提高模型的求解效率．采用近似射线步既能减小计算量又能使迭代过程更加平稳，采用删除无效约束技术能减小优化模型的规模. 以MSC/Nastran软件为结构分析的求解器，以MSC/Patran软件为开发平台，完成了满足刚度和强度的多工况、多变量的框架截面优化软件．算例结果表明上述程序算法的高效性．
- 框架结构 /
- 截面优化 /
- 对偶二次规划 /
- 近似射线步 /
- 删除无效约束
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.
- frame structure /
- sectional optimization /
- dual-quadratic programming /
- approximate scaling step /
- deletion of negative constraint

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参考文献(12)

[1]	Schmit L A. Structural design by systematic synthesis[A].In:Proceedings of the Second National Conference on Electronic Computation[C].New York: American Society of Civil Engineering,1960,105—132.
[2]	Prager W,Taylor J E.Problems of optimal structural design[J].Journal of Applied Mechanics,1968,35(1):102—106. doi: 10.1115/1.3601120
[3]	Prager W,Shield R T.A general theory of optimal plastic design[J].Journal of Applied Mechanics,1967,34(1):184—186. doi: 10.1115/1.3607621
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[9]	Rozvany G I N, ZHOU Ming. COC algorithm, Part Ⅰ:cross-section optimization or sizing[J].Computer Methods in Applied Mechanics and Engineering,1991,89(1/3):281—308. doi: 10.1016/0045-7825(91)90045-8
[10]	ZHOU Ming, Rozvany G I N. DCOC: An optimality criteria method for large system. Part Ⅰ: theory[J].Structure Optimization,1992,5(1):12—25. doi: 10.1007/BF01744690
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[12]	隋允康.建模·变换·优化——结构综合方法新进展[M].大连：大连理工大学出版社，1996，87—177.

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基于对偶二次规划的大型框架结构优化方法

作者简介:
隋允康(1943- ),男,辽宁大连人,教授,博导生导师(联系人.Tel:+86-10-67392239;Fax:+86-10-67392399;E-mail:ysui@bjut.edu.cn).

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Method Based on Dual-Quadratic Programming for Frame Structural Optimization With Large Scale

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基于对偶二次规划的大型框架结构优化方法

作者简介: 隋允康(1943- ),男,辽宁大连人,教授,博导生导师(联系人.Tel:+86-10-67392239;Fax:+86-10-67392399;E-mail:ysui@bjut.edu.cn).

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出版历程

Method Based on Dual-Quadratic Programming for Frame Structural Optimization With Large Scale

计量

出版历程

目录

作者简介:
隋允康(1943- ),男,辽宁大连人,教授,博导生导师(联系人.Tel:+86-10-67392239;Fax:+86-10-67392399;E-mail:ysui@bjut.edu.cn).