基于混合式过滤策略的结构拓扑优化方法
Structural Topology Optimization Based on the Improved Hybrid Filter Method
摘要: 为了有效解决拓扑优化过程中所存在的棋盘格与灰度单元等数值不稳定问题，提出一种基于混合式过滤策略的结构拓扑优化方法。该方法首先构建了基于混合式拓扑优化密度插值模型，保证了其在设计域的连续性，从数学本质上可消除棋盘格现象；然后在传统优化准则中叠加灰度过滤策略，提出一种灵敏度过滤和灰度过滤相结合的改进过滤技术，从而实现结构的拓扑更新，该方法能有效抑制灰度单元；最后通过三个典型数值算例进一步验证了本文方法的可行性和有效性。
Abstract: In order to effectively solve the numerical instability problems of topology optimization, such as checkerboard and grayscale elements, a new structural topology optimization method based on improved hybrid filter method is proposed. Firstly, a density interpolation model based on bi-linear function is constructed. It eliminates the checkerboard phenomenon from the mathematical essence because of its continuity in the design domain; Secondly, a grayscale filtering strategy is imposed on the traditional optimization criterion, and an improved filtering technique combining sensitivity filtering and grayscale filtering is also proposed. Based on the method, the topology structure is updated and the gray unit can be effectively suppressed. Finally, the feasibility and effectiveness of the method are verified by three typical numerical examples.
文章引用：欧阳华兵. 基于混合式过滤策略的结构拓扑优化方法[J]. 机械工程与技术, 2019, 8(6): 466-475. https://doi.org/10.12677/MET.2019.86054

参考文献

[1] Wang, F., Lazarov, B.S., Sigmund, O. and Søndergaard Jensen, J. (2014) Interpolation Scheme for Fictitious Domain Techniques and Topology Optimization of Finite Strain Elastic Problems. Computer Methods in Applied Mechanics and Engineering, 276, 453-472. [Google Scholar] [CrossRef] 
[2] Liu, J., et al. (2018) Current and Future Trends in Topology Optimization for Additive Manufacturing. Structural and Multidisciplinary Optimization, 57, 2457-2483. [Google Scholar] [CrossRef] 
[3] Bendsøe, M.P. and Kikuchi, N. (1988) Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering, 71, 197-224. [Google Scholar] [CrossRef] 
[4] 陈拥平, 高亮, 肖蜜. 基于变密度法的散热结构拓扑优化设计[J]. 计算机集成制造系统, 2018, 24(1): 117-126.
[5] Hardjasaputra, H. (2015) Evolutionary Structural Optimization as Tool in Finding Strut-and-Tie-Models for Designing Reinforced Concrete Deep Beam. Procedia Engineering, 125, 995-1000. [Google Scholar] [CrossRef] 
[6] van Dijk, N.P., Maute, K., Langelaar, M. and van Keulen, F. (2013) Level-Set Methods for Structural Topology Optimization: A Review. Structural and Multidisciplinary Optimization, 48, 437-472. [Google Scholar] [CrossRef] 
[7] Groenwold, A.A. and Etman, L.F.P. (2009) A Simple Heuristic for Gray-Scale Suppression in Optimality Criterion-Based Topology Optimization. Structural and Multidisciplinary Optimization, 39, 217-225. [Google Scholar] [CrossRef] 
[8] Sigmund, O. and Maute, K. (2013) Topology Optimization Approaches: A Comparative Review. Structural and Multidisciplinary Optimization, 48, 1031-1055. [Google Scholar] [CrossRef] 
[9] Sigmund, O. (2007) Morphology-Based Black and White Filters for Topology Optimization. Structural and Multidisciplinary Optimization, 33, 401-424. [Google Scholar] [CrossRef] 
[10] 龙凯, 傅晓锦. 考虑密度梯度的敏度过滤方法[J]. 计算机辅助设计与图形学学报, 2014, 26(4): 669-674.
[11] 杜义贤, 张严, 李涵钊. 具有逼近0/1离散特性的拓扑优化迭代算法[J]. 机械设计与研究, 2017, 33(1): 58-62.
[12] 朱剑峰, 等. 连续体结构拓扑优化改进的敏度修正方法研究[J]. 中国机械工程, 2014(11): 1506-1510.
[13] 昌俊康, 段宝岩. 连续体结构拓扑优化的一种改进变密度法及其应用[J]. 计算力学学报, 2009, 26(2): 188-192.
[14] Sigmund, O. (2001) A 99 Line Topology Optimization Code Written in Matlab. Structural and Multidisciplinary Optimization, 21, 120-127. [Google Scholar] [CrossRef] 
[15] Philip Bendsoe, M. and Sigmund, O. (2003) Topology Optimization: Theory, Methods and Applications. Springer, Berlin.

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