不确定载荷下的桁架结构拓扑优化

李东泽; 于登云; 马兴瑞

不确定载荷下的桁架结构拓扑优化

1.
北京空间飞行器总体设计部北京 100094
2. 中国空间技术研究院北京 100094
3. 中国航天科技集团公司北京 100037

基金项目: 国家973基金资助项目

详细信息

作者简介:
李东泽(1973-),男,吉林长春人,博士生,Dongze_li@hotmail.com.

中图分类号: O 327
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- 被引次数: 0
出版历程
- 收稿日期: 2008-09-30
- 网络出版日期: 2009-10-31

Truss topology optimization with uncertain loading scenarios

1.
Beijing Institute of Spacecraft System Engineering, Beijing 100094, China
2. China Academy of Space Technology, Beijing 100094, China
3. Chinese Space Science and Technology Group Co, Beijing 100037, China

摘要

摘要: 对带有不确定扰动载荷的桁架结构拓扑优化问题进行了研究.将不确定载荷表示成有界凸集,从而把不确定性问题转化为一个确定性问题.构造了凸集载荷下以体积为约束的柔度最小化模型,该优化模型的实质是在高维椭球内计算最大柔度最小问题.由于采用传统优化模型存在计算上的困难,对凸集载荷进行了数学处理,并据此构造了半定规划形式的优化模型以便求解.优化结果相对于给定载荷的刚度虽然略低,但对不确定的扰动载荷却具有一定的承载能力.算例表明通过半定规划法构造的考虑扰动载荷作用下的优化结果鲁棒性较佳,结构形式更接近于实际工程结构.
- 桁架 /
- 拓扑优化 /
- 不确定载荷 /
- 鲁棒
Abstract: A new model of truss topology optimization (TTO) considering uncertain (in size and direction) loading scenarios was presented. The uncertain loading was modeled as bounded convex sets, and the uncertain model was transformed to a deterministic model. The TTO was formulated as minimization of the compliance subject to volume constraints, and the nature of this type of optimization is to minimizing maximum compliance in high dimensional ellipsoid. The traditional model considering convex sets is hard to solve, and TTO with convex sets was modeled as semidefinite programming (SDP) to overcome this special difficulty. The compliance both to given loading scenarios and a small occasional was simultaneously optimized in SDP model and optimum result showed that the compliance of the truss were slightly reduced respect to given loads, but the optimum topology of the truss is more robust and more practical than that with non-uncertain loading scenarios from the engineering viewpoints.
- truss design /
- topology optimization /
- uncertain loading /
- robustness

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参考文献(1)

[1] Ben-Tal A, Nemirovski A. Robust optimization-methodology and applications [J]. Math Program, 2002, B92:453-480 [2] Kharmanda G, Olhoff N, Mohamed A, et al. Reliability-based topology optimization [J]. Structural and Multidisciplinary Optimization, 2004, 26:295-307 [3] Yi Ping, Cheng Gengdong. Further study on efficiency of sequential approximate programming for probabilistic structural design optimization [J]. Structural and Multidisciplinary Optimization, 2008,35:509-522 [4] Ben-Tal A, Ghaoui L El, Nemirovski A. Robust semidefinite programming Wolkowicz H, Saigal R, Vandenberghe L. Handbook on Semidefinite Programming. Netherlands:Kluwer Academic Publishers, 2000 [5] Ben-Tal A, Bendsoe M P. A new method for optimal truss topology design [J]. SIAM Journal on Optimization, 1993, 3:322-358 [6] Wolkowicz H, Saigal R, Vandenberghe L. Handbook of semidefinite programming: theory, algorithms, and applications [M]. Netherlands: Kluwer Academic Publishers, 2000 [7] Chaerani D. Modeling robust design problems via conic optimization . The Netherlands: Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology, 2006 [8] Ben-Tal A, Nemirovski A. Robust convex optimization [J]. Math Oper Res, 1998, 23(4):769-805 [9] Potra F A, Sheng R. A superlinearly convergent primal-dual infeasible interior point algorithm for semidefinite programming [J]. SIAM Journal on Optimization, 1998, 8(4):1007-1028 [10] Ghaoui El L, Lebret O F. Robust solutions to uncertain semidefinite programs [J]. SIAM Journal on Optimization, 1998, 9:33-52

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