• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (13): 47-56.doi: 10.3901/JME.2018.13.047

• 特邀专栏:柔性机构及机器人 • 上一篇    下一篇

基于序列插值模型和多重网格方法的多材料柔性机构拓扑优化

杜义贤1,2, 李涵钊1,2, 谢黄海1,2, 田启华1,2, 周祥曼1,2, 罗震3   

  1. 1. 三峡大学机械与动力学院 宜昌 443002;
    2. 水电机械设备设计与维护湖北省重点实验室 宜昌 443002;
    3. 悉尼科技大学电机、机械和机械电子系统工程学院 悉尼 NSW2007 澳大利亚
  • 收稿日期:2017-07-09 修回日期:2017-11-22 出版日期:2018-07-05 发布日期:2018-07-05
  • 通讯作者: 杜义贤(通信作者),男,1978年出生,博士,教授。主要研究方向为结构优化与分析、CAD/CAM技术。E-mail:duyixian@aliyun.com
  • 作者简介:李涵钊,男,1990年出生,硕士研究生。主要研究方向为结构优化与分析、轻量化设计、材料/结构一体化设计。E-mail:lihanzhao@aliyun.com
  • 基金资助:
    国家自然科学基金(51775308,51705287,51475265)、湖北省科技支撑计划对外科技合作(2015BHE026)和湖北省教育厅科学研究计划(D20161205)资助项目。

Topology Optimization of Multiple Materials Compliant Mechanisms Based on Sequence Interpolation Model and Multigrid Method

DU Yixian1,2, LI Hanzhao1,2, XIE Huanghai1,2, TIAN Qihua1,2, ZHOU Xiangman1,2, LUO Zhen3   

  1. 1. College of Mechanical & Power Engineering, China Three Gorges University, Yichang 443002;
    2. Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, Yichang 443002;
    3. School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney NSW2007, AU
  • Received:2017-07-09 Revised:2017-11-22 Online:2018-07-05 Published:2018-07-05

摘要: 基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)的多材料柔性机构拓扑优化是将原问题分解成若干子问题进行分层优化,成倍地增加了设计变量数量,且该方法利用传统的有限元离散,为了得到清晰的拓扑结构网格数量必然巨大,这两方面的因素造成了该方法计算效率低下。因此,基于幂函数多项式提出序列插值模型,用该模型进行多材料布局迭代,使不同材料在设计域内序列向预定义的多个材料点聚集,无须分解成子问题即可在单一优化框架下完成多材料的拓扑优化,且没有增加设计变量数量。以机构的几何增益最大为目标,建立多材料柔性机构拓扑优化模型。在利用有限元求解控制方程过程中引入多重网格方法,网格划分粒度层次递进,将粗网格水平下位移场作为细网格上的初始场量,避免直接用细密网格将设计域整体离散带来的高计算成本问题,提升计算效率。通过改进的优化准则法求解模型,得到序列最优布局型式的多材料柔性机构。通过典型算例及与基于SIMP的方法相应结果对比,验证了提出方法的有效性。

关键词: 多材料, 多重网格方法, 柔性机构, 拓扑优化, 序列插值模型

Abstract: The topological optimization of multi-material compliant mechanism based on solid isotropic material with penalization (SIMP) interpolation model is to decompose the original problem into a hierarchy of single material sub-optimization, the design variables are doubled, and the number of structural grids is bound to be huge to get clear configuration when the traditional finite element method is used, the inefficiency of the method are caused by these two factors. Therefore, the sequence interpolation model is proposed based on power function polynomial to iterate the layout of multiple materials, so that the ordered density of different material gathered to the predefined numbers of material points in the design domain without any decomposition and increasing of design variables in a single optimization framework to realize multi-material topology optimization. The optimization model of multi-material compliant mechanism is established based on the geometrical advantage of the mechanism. In the process of solving the control equation by using the finite element method, the multigrid method is imposed, the meshing granularity is progressive, and the displacement field under the coarse grid level is taken as the initial field on the finer grid without any unnecessary high computational costs by overall discrete of the design domain. The computational efficiency is greatly improved. The optimal layout pattern of multi-material compliant mechanism is obtained by using the modified optimality criterion method. Widely studied numerical examples are conducted and compared with the corresponding results of SIMP method, which demonstrate the effectiveness of the proposed method.

Key words: compliant mechanism, multigrid method, multiple materials, sequence interpolation model, topology optimization

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