力学学报 ›› 2018, Vol. 50 ›› Issue (3): 611-621.doi: 10.6052/0459-1879-17-366

• 固体力学 • 上一篇    下一篇

考虑破损-安全的连续体结构拓扑优化ICM方法

彭细荣1, 隋允康2, *   

  1. 1 湖南城市学院土木工程学院,湖南益阳 413000;
    2 北京工业大学工程数值模拟中心,北京 100022
  • 收稿日期:2017-11-07 出版日期:2018-05-15 发布日期:2018-06-11
  • 通讯作者: 隋允康 , 教授, 主要研究方向:结构优化. E-mail:ysui@bjut.edu.cn
  • 作者简介:彭细荣,副教授,主要研究方向:结构优化. E-mail:pxr568@163.com
  • 基金资助:

    国家自然科学基金(11672103)和湖南省自然科学基金(2016JJ6016)资助项目.

ICM METHOD FOR FAIL-SAFE TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES

Peng Xirong1, Sui Yunkang2, *   

  1. 1 School of Civil Engineering, Hunan City University, Yiyang 413000, Hunan, China;
    2 Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100022, China
  • Received:2017-11-07 Online:2018-05-15 Published:2018-06-11

摘要:

本文瞄准连续体在破损-安全考虑下的结构拓扑优化问题,旨在克服传统模型求解所得最终构型存在的弊病,避免结构因缺乏合理的冗余结构而敏感于局部破坏,实现破损-安全的目标. 首先,梳理了以往虽然用到却并不明晰的4个概念:结构局部破损模式、结构局部破损区域、结构破损状况、结构破损状况的预估分布. 之后,基于独立连续映射(ICM)方法,对该问题建立了力学性能约束下结构体积极小化的模型. 建立目标函数时,利用Minimax的概念将可能出现的结构破损状况对应的所有结构体积目标转化为原结构的唯一结构体积目标,克服了多目标问题的困难. 建立近似约束函数时,将可能出现的所有结构破损状况对应的力学性能的约束皆考虑进去,既能处理载荷单工况也能处理载荷多工况. 最后,以位移约束为例,建立了优化模型并求解. 单工况及多工况位移约束拓扑优化算例验证了算法的有效性. 结果表明:本方法相比于不考虑破损-安全的拓扑优化设计,得到的最优拓扑更复杂,体积比更大即所用材料更多,亦即最优结构具有更多的冗余,此正是考虑破损-安全设计原则的结果. 本文的研究对于航空、航天、其他水、陆等领域运载工具以及其他工程结构在意外破坏、战争创伤或恐怖袭击下的结构设计,乃是非常重要的进展.

关键词:

连续体结构|拓扑优化|破损-安全|ICM方法

Abstract:

Aimed at the topology optimization of continuum structures considering the fail-safe principle, for the purpose of overcoming the shortcomings of the topologies obtained by the traditional topology optimization being too sensitive to local damages for the lack of reasonable redundancy components, the fail-safe design is achieved. At first, four concepts are clarified: the structural local failure mode, the structural local failure region, structural failure case, and the pre-estimation distribution of structural failure cases. Secondly, based on the ICM (independent continuous mapping) method, a minimizing structural volume model with structural performance constraints is established for the fail-safe topology optimization problems of continuum structures. While establishing the objective function, minimizing the maximum of structural volumes of all structural failure cases is converted into minimizing the structural volume of the ground structure without failure regions. Therefore, the difficulty of dealing with multi-objective optimization is avoided. While establishing the approximation functions of constraints, mechanical property constraints of all of the structural failure cases are taken into account. The problems with a single load case or multi-load cases can be solved by the presented model. At last, optimization problems with displacement constraints are taken as examples. The optimization model is established and the solution method is also presented. Some examples with displacement constraints under a single load case or multi-load case are presented to verify the validity of this method. The results show that the optimal topologies obtained by this method are more complex and has a greater volume than that obtained by the topology optimization without fail-safe. Namely, optimal topologies have more redundancy, which is the result of considering the fail-safe principle. The proposed research is an important progress for the design of vehicles serving for aviation, aerospace, water or land fields and other engineering structures undergoing accident damages, war wounds or terrorist attacks.

Key words:

continuum structures|topology optimization|fail-safe|ICM method

中图分类号: 

  • O343.1