基于能量均匀化的高剪切强度周期性点阵结构拓扑优化

doi:10.3901/JME.2017.18.152

机械工程学报 ›› 2017, Vol. 53 ›› Issue (18): 152-160.doi: 10.3901/JME.2017.18.152

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基于能量均匀化的高剪切强度周期性点阵结构拓扑优化

杜义贤^1,2, 李涵钊¹, 田启华^1,2, 尹艺峰¹, 罗震³

1. 三峡大学机械与动力学院宜昌 443002;
2. 三峡大学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:2016-09-24 修回日期:2017-05-05 出版日期:2017-09-20 发布日期:2017-09-20
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 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;田启华,男,1962年出生,博士,教授.主要研究方向为机械设计及理论、CAD/CAM与制造业信息化等.E-mail:tqh@ctgu.edu.cn
基金资助:
国家自然科学基金（51105229，51475265）、湖北省杰出青年基金（2013CFA022）、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 Periodic Lattice Structure with High Shear Strength Using Energy-based Homogenization

DU Yixian^1,2, LI Hanzhao¹, TIAN Qihua^1,2, YIN Yifeng¹, LUO Zhen³

1. College of Mechanical & Power Engineering, China Three Gorges University, Yichang 443002;
2. Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, China Three Gorges University, Yichang 443002;
3. School of Electrical, Mechanical and Mechatronic Systems, University of Technology Sydney, Sydney NSW2007, Australia

Received:2016-09-24 Revised:2017-05-05 Online:2017-09-20 Published:2017-09-20

摘要/Abstract

摘要： 传统多孔结构构型型式单一、缺乏科学设计方法的指导，为了从拓扑构型角度设计抗剪切性能更优的周期性点阵结构，基于拓扑优化技术，以周期性单胞为研究对象，以其切变模量最大为目标，以结构的材料用量和力学控制方程为约束条件，利用能量均匀化方法建立基于宏观力学性能的细观点阵结构的优化模型，通过改进的优化算法求解模型，得到了一种宏观上的拓扑边界清晰的周期性点阵结构。然后根据优化结果，在考虑胞元非等壁厚和横向剪切变形影响条件下进行等效材料力学性能分析，得到剪切性能关于微结构胞元几何参数的表征，同时加工制造了优化得到的周期性点阵结构，并进行了剪切力学性能测试。从理论分析和性能试验两个方面与六边形蜂窝结构相应的切变模量进行对比，结果表明，经优化得到的周期性点阵结构切变模量有大幅提升、抗剪切性能更优越。验证了所提出方法能有效地应用于周期性点阵结构抗剪切性能的优化设计。

关键词: 点阵结构, 高剪切强度, 能量均匀化方法, 拓扑优化

Abstract: The topology configuration of traditional porous structure is single, lack of scientific design method for guidance. In order to design periodic lattice structure with high shear strength. The optimization model of micro-cellular materials based on the properties of macrostructures which focused on the periodic base cell for finding a micro-structural topology with the maximum shear modulus under a prescribed volume and mechanic constraint is built based on topology optimization technique. By solving the model on modified optimal algorithm, the mechanical equivalent properties are deduced according to the optimized result, the characterization of shear performance with respect to microstructural geometrical parameters is obtained by considering the transverse shear deformation and the flexibility of the cell wall. Finally, the obtained lattice structure is manufactured, and then the shear properties are tested, it can be concluded that the measured shear modulus of the lattice structure is higher than those of hexagonal honeycomb structures, which demonstrates the excellence shearing performance of the periodic lattice structure. Results show that the proposed method can be effectively applied to the design of periodic lattice structure with great shear performance.

Key words: energy-based homogenization method, high shear strength, lattice structure, topology optimization

中图分类号:

TH11

杜义贤, 李涵钊, 田启华, 尹艺峰, 罗震. 基于能量均匀化的高剪切强度周期性点阵结构拓扑优化[J]. 机械工程学报, 2017, 53(18): 152-160.

DU Yixian, LI Hanzhao, TIAN Qihua, YIN Yifeng, LUO Zhen. Topology Optimization of Periodic Lattice Structure with High Shear Strength Using Energy-based Homogenization[J]. Journal of Mechanical Engineering, 2017, 53(18): 152-160.

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基于能量均匀化的高剪切强度周期性点阵结构拓扑优化

Topology Optimization of Periodic Lattice Structure with High Shear Strength Using Energy-based Homogenization

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