桁架拓扑优化几何稳定性判定法和约束方案比较

郝宝新; 周志成; 曲广吉; 李东泽

doi:10.13700/j.bh.1001-5965.2018.0624

桁架拓扑优化几何稳定性判定法和约束方案比较

doi: 10.13700/j.bh.1001-5965.2018.0624

中国空间技术研究院, 北京 100094

基金项目:

国家自然科学基金 11402281

详细信息

作者简介:
郝宝新  男, 博士研究生。主要研究方向:航天器结构优化设计

周志成  男, 博士, 研究员, 博士生导师, 中国工程院院士。主要研究方向:航天器总体设计、航天器动力学

曲广吉  男, 研究员。主要研究方向:航天器动力学与控制、航天器总体设计

李东泽  男, 博士, 高级工程师。主要研究方向:航天器总体设计、航天器结构优化设计

通讯作者:
周志成, E-mail: zhouzhicheng@cast.cn

中图分类号: O224;TU323.4
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出版历程
- 收稿日期: 2018-10-29
- 录用日期: 2019-04-15
- 网络出版日期: 2019-08-20

Comparison of determining methods and constraint schemes for geometric stability in truss topology optimization

China Academy of Space Technology, Beijing 100094, China

Funds:

National Natural Science Foundation of China 11402281

More Information

Corresponding author: ZHOU Zhicheng, E-mail: zhouzhicheng@cast.cn

摘要

摘要:
为提高桁架结构几何稳定性的判定准确度和桁架拓扑优化结果的工程实用性，对桁架结构几何稳定性的判定方法和桁架结构拓扑优化问题中3种几何稳定约束方案的有效性进行了比较研究。首先结合简单桁架示例，对比了判定桁架结构几何稳定性的几种方法，给出评估桁架结构几何稳定性的一种简单流程；然后对处理桁架结构几何稳定性的3种常见约束方案，给出了对应拓扑优化问题的一个统一的半定规划（SDP）模型；最后结合算例讨论了3种几何稳定约束方案下的拓扑优化结果，说明了不同方案的有效性。结果表明，考虑附加载荷或全局稳定约束均不能保证优化后桁架结构的几何稳定性，但在约束值合理设置的情况下，考虑基频约束则可以保证。
- 桁架拓扑优化 /
- 几何稳定性 /
- 半定规划(SDP) /
- 附加载荷 /
- 基频约束 /
- 全局稳定约束
Abstract:
To improve the accuracy of determining truss geometric stability and the practicability of truss topology optimization results, several ways of determining truss geometric stability were compared, and the validity of three schemes for guaranteeing truss geometric stability of topology optimization results were discussed. First, by comparing several ways to identify truss geometric stability through some illustrative tiny trusses, a simple procedure was outlined to evaluate truss geometric stability. Second, a unified semidefinite programming (SDP) formulation of the truss topology optimization problem was established for three kinds of constraints to address the geometric stability issue. Finally, three truss structures were optimized with the SDP formulation, and the geometric stabilities of the resultant trusses were evaluated by the given simple scheme to reveal the validity of the three kinds of constraints to guarantee geometric stability. The results show that considering additional loads or the global stability constraint cannot guarantee the geometric stability of the optimized trusses while the fundamental frequency constraint can do when the constraint values are reasonably chosen.
- truss topology optimization /
- geometric stability /
- semidefinite programming (SDP) /
- additional loads /
- fundamental frequency constraint /
- global stability constraint

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图 1 桁架结构几何稳定性的判定流程

Figure 1. Flowchart for determining truss geometric stability

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图 2 10杆桁架基结构及不同工况下优化后的拓扑

Figure 2. 10-bar truss ground structure and optimized topologies under different load combinations

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图 3 33杆桁架基结构及不同基频约束下优化后的拓扑

Figure 3. 33-bar truss ground structure and optimized topologies under different fundamental frequency constraints

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图 4 33杆桁架不合理基频约束下的拓扑优化结果

Figure 4. Topology optimization results of 33-bar truss under unreasonable fundamental frequency constraints

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图 5 4杆桁架基结构及不同约束和载荷值下的拓扑优化结果

Figure 5. 4-bar truss ground structure and topology optimization results under different constraints and loads

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图 6 88杆桁架基结构及不同设定下优化后的拓扑

Figure 6. 88-bar truss ground structure and optimized topologies under different settings

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表 1 不同方法对几何稳定性的判定结果

Table 1. Geometric stability determined by different methods

编号	拓扑	方法1)	方法2)	方法3)	方法4)	n_DOF	k_DOF
1		×	×	×	×	2	2
2		√	×	×	×	1	1
3		√	×	×	×	1	1
4		×	√	×	×	0	1

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表 2 88杆桁架基结构及优化结果特性

Table 2. Properties of ground structure and optimized topologies for 88-bar truss

结构	杆数	体积	几何稳定	柔度	基频	临界屈曲载荷因子
基结构	88	157	是	0.03	0.080 9	64.244^*
图 6(b)	22	66.879	否(N20)	0.03		307.39
图 6(c)	42	67.704	否(N3)	0.03		1.133 8
图 6(d)	55	67.392	是	0.03	0.079 5	0.548 9
图 6(e)	41	66.927	否(N8)	0.03		0.869 1
注：*表示本文分析所得基结构的临界屈曲载荷因子为64.244，与Nastran分析结果一致；文献[14]中该数据值为1.074，疑有误。

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