面向增材制造的应力最小化连通性拓扑优化

王超; 徐斌; 段尊义; 荣见华

doi:10.6052/0459-1879-20-389

面向增材制造的应力最小化连通性拓扑优化

doi: 10.6052/0459-1879-20-389

王超^*,
徐斌^*, ,,
段尊义^*,
荣见华^†

^*西北工业大学力学与土木建筑学院, 西安 710072
^†长沙理工大学汽车与机械工程学院, 长沙 410114

基金项目: 1)国家自然科学基金(11872311);国家自然科学基金(11772070);陕西省自然科学基金(2020JM085)

详细信息

作者简介:
2)徐斌, 教授, 主要研究方向: 结构拓扑优化, 结构动力学与控制. E-mail: xubin@nwpu.edu.cn

通讯作者:
徐斌

中图分类号: O343
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出版历程
- 收稿日期: 2020-11-18
- 刊出日期: 2021-04-10

ADDITIVE MANUFACTURING-ORIENTED STRESS MINIMIZATION TOPOLOGY OPTIMIZATION WITH CONNECTIVITY

Wang Chao^*,
Xu Bin^{*
, ,},
Duan Zunyi^*,
Rong Jianhua^†

^*School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi'an 710072, China
^†School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, China

摘要

摘要: 增材制造与拓扑优化的有机结合将极大促进高性能产品的研发, 但现有基于拓扑优化的设计性能和可制造性研究多是独立开展, 或常局限于传统的刚度问题, 缺乏对工程中至关重要的强度问题的考虑. 面向增材制造, 针对协同考虑强度和可制造连通性的结构优化问题, 建立了材料体积和连通性标量场约束下的结构应力最小化拓扑优化模型. 针对求解过程中的不同数值困难问题, 提出了有效的优化求解策略. 引入基于P范数的全局标量场约束度量, 并结合稳定转换误差修正技术来实现对局部标量场的有效控制. 详细推导了相关灵敏度, 然后通过典型数值算例论证了文中模型及方法的合理有效性. 结果表明, 仅考虑连通性约束的刚度最大化设计不一定能避免局部高应力集中, 而该设计也不一定等同于应力最小化连通性设计; 充足的材料许用量和恰当的连通性约束边界条件对提高所研究设计的性能至关重要, 而应力凝聚参数取值并非越大越好, 合理取值才能有助于获取高性能设计. 此外, 优化结果也在一定程度上论证了可制造性拓扑优化中考虑强度问题的必要性和可行性.
- 拓扑优化 /
- 增材制造 /
- 应力最小化 /
- 连通性约束 /
- 灵敏度分析
Abstract: The organic combination of additive manufacturing and topology optimization will greatly promote the development of high-performance products. However, most of the existing researches on design performance and manufacturability based on topology optimization are carried out separately. And, they often focus on traditional stiffness problems and lack the consideration of the most important strength problems in practical engineering. In this paper, an additive manufacturing-oriented topology optimization model for the structural optimization problem that considers strength and manufacturability connectivity collaboratively is established, viz, a structural stress minimization under material volume and connectivity-based scalar field constraints. An effective optimization strategy is introduced to overcome various numerical problems in the solution. The P-norm based global scalar field constraint measure is employed, together with the stability transformation method-based error correction technique to realize the effective control of the local scalar field. The corresponding sensitivity is derived in detail. The rationality and effectiveness of the proposed model and method are demonstrated by typical numerical examples. Optimized results show that the stiffness maximization design considering only the connectivity constraint may not necessarily avoid local high stress concentration, and the design is not necessarily equivalent to the stress minimization connectivity design. Sufficient material allowance and appropriate connectivity constraint boundary conditions are important to improve the performance of the design studied. Moreover, the value of the stress aggregation parameter is not the bigger the better, only a reasonable value can help to obtain a high-performance design. To some extent, the results also demonstrate the necessity and feasibility of considering the strength problem in manufacturing-oriented topology optimization.
- topology optimization /
- additive manufacturing /
- stress minimization /
- connectivity constraint /
- sensitivity analysis

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