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工程设计学报
Chin J Eng Design  2022, Vol. 29 Issue (3): 279-285    DOI: 10.3785/j.issn.1006-754X.2022.00.039
Design Theory and Method     
Research on variable density topology optimization method for continuum structure
Jing-liang WANG1(),Tian-cheng ZHU2,Long-biao ZHU3,Fei-yun XU4
1.School of Marine Electrical and Intelligent Engineering, Jiangsu Maritime Vocational Institute, Nanjing 211100, China
2.Jiangsu Branch, China United Network Communications Group Co. , Ltd. , Nanjing 211100, China
3.School of Mechanical Engineering, Nantong University, Nantong 226019, China
4.School of Mechanical Engineering, Southeast University, Nanjing 211100, China
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Abstract  

In order to achieve the topological optimization of the volume constraint and the minimum compliance of the continuous structure and solve the numerical instability problems, such as gray-scale element and checkerboard grid caused by classical variable density method, a new topology optimization method was proposed. Firstly, the method of improved solid isotropic material with penalization was used as the material interpolation scheme to establish a structural topology optimization model；secondly, the numerical instability problem was solved by introducing sensitivity filtering method based on the Gaussian weight function and designing a new gray-scale element suppression operator; finally, the optimization model was solved by the optimality criterion method. Through example analysis, it could be seen that the new strategy could improve the topology optimization method. The method had the advantages of faster convergence, acquisition of optimized structures with small compliance and good topological configuration and better suppression of gray-scale element generation. The results provide new ideas for the study of topological optimization of other continuum structures.

Key words： continuum structure      topology optimization method      method of solid isotropic materials      with penalization sensitivity filtration method      gray-scale element suppression operator     
Received: 08 August 2021      Published: 05 July 2022
CLC:  TH 122  
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Jing-liang WANG
Tian-cheng ZHU
Long-biao ZHU
Fei-yun XU
Cite this article:

Jing-liang WANG,Tian-cheng ZHU,Long-biao ZHU,Fei-yun XU. Research on variable density topology optimization method for continuum structure. Chin J Eng Design, 2022, 29(3): 279-285.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.039     OR     https://www.zjujournals.com/gcsjxb/Y2022/V29/I3/279


连续体结构的变密度拓扑优化方法研究

为了实现使连续体结构的体积约束和柔顺度最小的拓扑优化及解决采用经典变密度法引起的结构优化结果存在如灰度单元、棋盘格等数值不稳定问题，提出了一种新的拓扑优化方法。首先，采用改进的固体各向同性材料惩罚法作为材料插值方案，建立结构拓扑优化模型；其次，通过引入基于高斯权重函数的敏度过滤法和设计新灰度单元抑制算子来解决数值不稳定问题；最后，借助优化准则法求解优化模型。通过算例分析可知：新策略可以改进拓扑优化方法；新的拓扑优化方法具有收敛速度较快、能更好地获取柔顺度小且拓扑构型好的优化结构和抑制灰度单元产生等优势。研究结果为其他连续体结构的拓扑优化研究提供了新思路。


关键词： 连续体结构,  拓扑优化方法,  固体各向同性材料惩罚法,  敏度过滤法,  灰度单元抑制算子 
Fig.1 MBB beam structure
Fig.2 Topological configuration of MBB beam structure under different SIMP methods
SIMP法c/（N·mm)I/次G/ %
文献[18]方法213.008326.66
本文方法208.546430.34
Table 1 Optimization results of MBB beam structure under different SIMP methods
Fig.3 Topological configuration of MBB beam structure under different sensitivity filtration methods
敏度过滤法c/（N·mm）I/次G / %
文献[18] 方法208.546430.34
本文方法205.836427.23
Table 2 Optimization results of MBB beam structure under different sensitivity filtration methods
Fig.4 Topological configuration of MBB beam structure under different gray-scale unit suppression operators
灰度单元抑制算子c/（N·mm）I/次G / %
文献[18] 方法205.836427.23
本文方法196.65353.89
Table 3 Optimization results of MBB beam structure under different gray-scale suppression operators
Fig.5 Topology configuration of MBB beam structure under different topology optimization methods
拓扑优化方法c/（N·mm）I/次G/ %
文献[14] 方法211.767224.27
文献[18] 方法213.008326.66
本文方法196.65353.89
Table 4 Optimization results of MBB beam structure under different topology optimization methods
Fig.6 Cantilever beam structure
Fig.7 Topological configuration of cantilever beam structure under different topology optimization methods
拓扑优化方法c/（N·mm）I/次G/ %
文献[14] 方法114.9011824.77
文献[18] 方法115.2316726.75
本文方法104.98384.73
Table 5 Optimization results of cantilever beam structure under different topology optimization methods
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