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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (11): 2169-2178    DOI: 10.3785/j.issn.1008-973X.2020.11.012
机械工程     
基于畸变比能全局化策略的应力拓扑优化
高云凯(),马超,刘哲,徐亚男
同济大学 汽车学院，上海 201804
Stress-based topology optimization based on global measure of distort energy density
Yun-kai GAO(),Chao MA,Zhe LIU,Ya-nan XU
School of Automotive Studies, Tongji University, Shanghai 201804, China
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摘要：

针对受体积约束的应力最小化连续体结构拓扑优化，提出一种改进的双向渐进结构优化方法. 使用Kreisselmeier-Steihauser函数建立畸变比能的全局化函数，以克服应力优化计算量大的难题. 利用伴随变量法求解单元灵敏度，并引入灵敏度过滤及修正方法稳定优化过程. 双向渐进结构优化方法通过逐渐增加和删除单元，使结构进化至最优构型. 3个典型的拓扑优化算例结果表明：提出的方法可有效提升应力拓扑优化的计算效率；与柔度最小化拓扑优化相比，使用适当的凝聚函数参数消除了结构中的应力集中效应，最优设计中的最大应力值较原设计有不同程度下降，提高了结构的强度. 双向渐进结构优化方法使用离散设计变量避免了应力奇异现象，拓扑优化结果的边界清晰.
关键词： 拓扑优化;  畸变比能;  凝聚函数;  双向渐进结构优化;  结构设计    
Abstract:

A modified bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of continuum structures was proposed. A global measure was formulated by Kreisselmeier-Steihauser aggregation function to reduce the computational cost. The sensitivity numbers were derived by the computationally efficient adjoint variable method. The optimization process was stabilized by a sensitivity filtering and correction scheme. Design variables were updated by BESO with its material addition and removal scheme that drove the initial structure gradually evolved to the optimal design. The effectiveness of the proposed method was verified by three representative numerical examples. The efficiency of the topology optimization process was significantly improved by the proposed method. Compared with the compliance minimization design, the proposed method with appropriate stress norm parameter can effectively alleviate stress concentration. The maximum stress values of the optimal designs showed various degrees of decrease, thus enhancing the strength of structures. BESO method using discrete variables avoids the stress singularity and obtains the black-and-white design.
Key words: topology optimization    distort energy density    aggregation function    bi-directional evolutionary structural optimization    structural design
收稿日期: 2019-12-17 出版日期: 2020-12-15
CLC:  O 342  
基金资助: 国家重点研发计划资助项目（2016YFB0101602）；国家自然科学基金资助项目（51575399）
作者简介: 高云凯（1963—），男，教授，博士，从事车身结构分析与优化设计研究. orcid.org/0000-0002-3486-059X. E-mail： gaoyunkai@tongji.edu.cn
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高云凯
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引用本文:

高云凯,马超,刘哲,徐亚男. 基于畸变比能全局化策略的应力拓扑优化[J]. 浙江大学学报(工学版), 2020, 54(11): 2169-2178.

Yun-kai GAO,Chao MA,Zhe LIU,Ya-nan XU. Stress-based topology optimization based on global measure of distort energy density. Journal of ZheJiang University (Engineering Science), 2020, 54(11): 2169-2178.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.11.012    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I11/2169

图 1  L型梁结构尺寸及边界条件示意图
图 2  L型梁优化结果及von Mises应力云图
图 3  L型梁体积分数及最大von Mises应力迭代历史
图 4  L型梁不同体积分数优化结果及最大von Mises应力
图 5  μ=10时L型梁的优化历程
图 6  MBB梁结构尺寸及边界条件示意图
图 7  MBB梁优化结果及von Mises应力云图
图 8  μ=10时MBB梁的优化历程
图 9  三维悬臂梁结构尺寸及边界条件示意图
图 10  三维悬臂梁优化结果及von Mises应力云图
图 11  μ=10时三维悬臂梁的优化历程
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