多位移约束下渐进结构拓扑优化设计

doi:10.16731/j.cnki.1671-3133.2017.08.004

现代制造工程 ›› 2017, Vol. 443 ›› Issue (8): 19-28.doi: 10.16731/j.cnki.1671-3133.2017.08.004

多位移约束下渐进结构拓扑优化设计

谢亚军¹, 荣见华^1,2, 俞燎宏^1,3, 朱海锋^1,3, 李方义^1,3

1 长沙理工大学汽车与机械工程学院,长沙 410076;
2 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室,长沙 410114;
3 长沙理工大学工程车辆安全性设计与可靠性技术湖南省重点实验室,长沙 410114

收稿日期:2016-02-19 出版日期:2017-08-20 发布日期:2018-01-09
作者简介:谢亚军,主要研究方向为汽车安全技术、结构轻量化设计。荣见华,主要研究领域为结构动力学设计、结构分析与优化设计等。E-mail:756651156@qq.com
基金资助:
国家自然科学基金项目(11372055,11302033)

Evolutionary structural topology optimization designs with multiple displacement constraints

Xie Yajun ¹, Rong Jianhua ^1,2, Yu Liaohong ^1,3, Zhu Haifeng ^1,3, Li Fangyi ^1,3

1 School of Automotive and Mechanical Engineering,Changsha University of Science and Technology,Changsha 410076,China;
2 Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle,Hunan Province,Changsha 410114,China;
3 Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle,Hunan Province,Changsha 410114,China

Received:2016-02-19 Online:2017-08-20 Published:2018-01-09

摘要/Abstract

摘要： 渐进结构优化方法通用性好,程序实现简单,能获得一系列黑白分布的优化拓扑,但它难于求解多约束拓扑优化问题。为了将渐进结构优化方法拓展到求解多约束拓扑优化问题,针对多位移约束下结构体积最小的结构拓扑优化问题,采用有理分式材料模型,建立刚度与拓扑变量的关系;构建求解多约束拉格朗日乘子的近似优化问题模型和其光滑对偶算法;而后,给出单元灵敏度数计算公式和渐进结构优化算法;最后给出了两个验证算例,所得结果验证了该方法的正确性和有效性。

关键词: 多位移约束, 渐进结构优化, 拓扑优化, 拉格朗日乘子

Abstract: The Evolutionary Structural Optimization(ESO) method is easily utilized to be programmed,and is of wide engineering applications,and may be adopted to obtain the optimum structure with black and white distribution material property.However,it’s difficult to solve the problem of multi-constrained topology optimization by using it.To extend this method to the case of multi-constrained topology optimization,for the problem of topology optimization with multiple displacement constraints,the relationship between the stiffness and the topology variables is built by using the Rational Approximation for Material Properties(RAMP),and a series of approximate models and a smooth dual algorithm are constructed to solve Lagrange multipliers.Then,the calculation formula of element sensitivities and a novel evolutionary structural optimization algorithm are given.Finally,two examples are presented to demonstrate the validity and effectiveness of the proposed method.

Key words: multiple displacement constraints, evolutionary structural optimization, topology optimization, Lagrange multiplier

中图分类号:

TH122

谢亚军, 荣见华, 俞燎宏, 朱海锋, 李方义. 多位移约束下渐进结构拓扑优化设计[J]. 现代制造工程, 2017, 443(8): 19-28.

Xie Yajun , Rong Jianhua , Yu Liaohong , Zhu Haifeng , Li Fangyi. Evolutionary structural topology optimization designs with multiple displacement constraints[J]. Modern Manufacturing Engineering, 2017, 443(8): 19-28.

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多位移约束下渐进结构拓扑优化设计

Evolutionary structural topology optimization designs with multiple displacement constraints

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