基于导重法的自重载荷下悬臂梁结构拓扑优化

任毅如; 向剑辉; 何杰; 宁克焱; 杨玲玲

doi:10.13700/j.bh.1001-5965.2020.0191

基于导重法的自重载荷下悬臂梁结构拓扑优化

doi: 10.13700/j.bh.1001-5965.2020.0191

1.
湖南大学机械与运载工程学院, 长沙 410082
2.
中国北方车辆研究所, 北京 100072

基金项目:

工业和信息化部基础产品创新科研项目 237099000000170008

详细信息

通讯作者:
任毅如. E-mail: renyiru@hnu.edu.cn

中图分类号: TP314;TH111;O343
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- 被引次数: 0
出版历程
- 收稿日期: 2020-05-18
- 录用日期: 2020-06-05
- 网络出版日期: 2021-07-20

Topology optimization of cantilever structure with self-weight load based on guide-weight method

1.
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
2.
China North Vehicle Research Institute, Beijing 100072, China

Funds:

Innovation Research Project of Basic Product of Ministry of Industry and Information Technology of China 237099000000170008

More Information

Corresponding author: REN Yiru. E-mail: renyiru@hnu.edu.cn

摘要

摘要:
针对自重载荷悬臂梁结构拓扑优化末端区域材料分布不收敛的问题，提出了一种拓扑优化方法。根据虚功相等原理，利用四节点矩形单元的形函数、单元体积密度和质量的关系建立了载荷等效方法。根据优化模型的Kuhn-Tucker条件推导出了导重准则，以及目标函数的灵敏度公式和考虑自重载荷拓扑优化的迭代算法。针对自重载荷作用下悬臂梁结构拓扑优化存在的末端区域材料分布模糊问题，研究了变密度法和非结构质量相结合的求解策略，揭示了典型因素对拓扑结构的影响规律。结果表明：所提方法能够解决自重载荷下悬臂梁末端区域材料分布模糊问题。
- 拓扑优化 /
- 导重法 /
- 变密度法 /
- 自重载荷 /
- 材料属性有理近似函数插值(RAMP)模型
Abstract:
Aiming at the problem of non-convergence of the material distribution at the end of the cantilever beam structure under self-weight load, a topology optimization method for the cantilever beam structure under self-weight load is proposed to solve the problem. According to the principle of virtual work equal, the load equivalent method was established by the relationship among the shape function of the four-node rectangular element, the unit volume density and the mass. According to the Kuhn-Tucker condition of the optimization model, the guide-weight criterion was derived, the sensitivity formula of the objective function was obtained, and the iterative formula considering the topology optimization of the self-weight load was derived. Aimed at the problem of ambiguity of material distribution in the end region of the topological optimization of a cantilever beam structure under self-weight load, a solution strategy combining variable density method and non-structural mass was studied, and the influence of typical factors on the topological structure was revealed. The results show that this method can solve the problem of fuzzy material distribution at the end of a cantilever beam under self-weight.
- topology optimization /
- guide-weight method /
- variable density method /
- self-weight load /
- Rational Approximation of Material Properties (RAMP) model

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图 1 自重载荷作用下的二维简支梁受力结构

Figure 1. Structural diagram of 2D simply supported beam under self-weight load

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图 2 待优化结构的有限元模型

Figure 2. Finite element model of structure to be optimized

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图 3 二维简支梁结构拓扑优化过程

Figure 3. Topology optimization process of 2D simply supported beam structure

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图 4 二维简支梁拓扑优化结果应力分析

Figure 4. Stress analysis of 2D simply supported beam topology optimization results

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图 5 优化前二维简支梁结构应力分析

Figure 5. Stress analysis of 2D simply supported beam structure before optimization

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图 6 自重载荷作用下结构应力分析

Figure 6. Structural stress analysis under self-weight load

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图 7 自重载荷作用下的二维悬臂梁结构示意图

Figure 7. Schematic diagram of 2D cantilever beam under self-weight load

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图 8 自重载荷作用下的二维悬臂梁拓扑优化结果

Figure 8. Topology optimization results of 2D cantileverbeam under self-weight load

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图 9 不同长高比下的悬臂梁拓扑优化结果

Figure 9. Topology optimization results of cantilever beams with different aspect ratios

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图 10 施加非结构质量的悬臂梁结构示意图

Figure 10. Schematic diagram of a cantilever beam with non-structural mass

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图 11 不同非结构质量情况下悬臂梁的拓扑优化结果

Figure 11. Topology optimization results of cantilever beams with different non-structural masses

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图 12 r=1悬臂梁拓扑优化结果应力分析

Figure 12. Stress analysis of r=1 cantilever beam topology optimization results

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图 13 r=0.1悬臂梁拓扑优化结果应力分析

Figure 13. Stress analysis of r=0.1 cantilever beam topology optimization results

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图 14 r=0.04悬臂梁拓扑优化结果应力分析

Figure 14. Stress analysis of r=0.04 cantilever beam topology optimization results

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表 1 悬臂梁结构自重载荷下应力峰值

Table 1. Peak stress of cantilever beam structure under self-weight load

非结构质量比值	峰值应力/MPa
1	10.15×10^-2
0.1	8.677×10^-2
0.04	6.219×10^-2

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