基于局部相对密度映射的变密度多孔结构设计方法

doi:10.3901/JME.2018.19.121

机械工程学报 ›› 2018, Vol. 54 ›› Issue (19): 121-128.doi: 10.3901/JME.2018.19.121

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基于局部相对密度映射的变密度多孔结构设计方法

赵芳垒, 敬石开, 刘晨燕

北京理工大学机械与车辆学院北京 100081

收稿日期:2017-10-21 修回日期:2018-06-05 出版日期:2018-10-05 发布日期:2018-10-05
通讯作者: 敬石开(通信作者),男,1975年出生,博士,副教授,硕士研究生导师。主要研究方向为产品创新设计、三维打印。E-mail:jingshikai@bit.edu.cn
作者简介:赵芳垒,男,1991年出生。主要研究方向为三维打印。E-mail:1579693293@qq.com
基金资助:
国家高技术研究发展计划（863计划，2015AA042505）。

Variable Density Cellular Structure Design Method Base on Local Relative Density Mapping

ZHAO Fanglei, JING Shikai, LIU Chenyan

School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081

Received:2017-10-21 Revised:2018-06-05 Online:2018-10-05 Published:2018-10-05

摘要/Abstract

摘要： 针对变密度多孔结构设计依据的拓扑优化密度信息不能被充分有效利用的问题，提出一种基于拓扑优化局部相对密度映射的变密度多孔结构设计方法。该方法根据多孔结构力学特点建立等效连续体的拓扑优化模型，通过拓扑优化密度的局部映射策略和调整方法，将拓扑优化的密度信息映射到多孔结构单元并根据映射的相对密度生成变密度多孔结构。此外，为检验多孔结构与拓扑优化密度信息的匹配程度，提出一种基于体素化和矩阵相似度的分析评价方法。最后以不同尺度的二维蜂窝为案例，验证了所提变密度多孔结构设计方法的可行性和有效性。

关键词: 变密度多孔结构, 局部相对密度映射, 矩阵相似度, 体素化, 拓扑优化

Abstract: To solve the problem that cellular structure design result cannot effectively reflect the topology optimization density information in the design process of variable density cellular structure, a variable density cellular structure design method based on topology optimization local relative density mapping strategy is proposed. According to the mechanics characteristics of cellular structure, the equivalent continuum solid topology optimization is established. The variable cellular structure can be constructed according to the cell's local relative density which is gained through unitizing local density mapping and density adjustment method. Besides, an analysis method is proposed to estimate matching relationship between the relativity density of topology optimization outcome and design outcome of cellular structure based on the voxelization and matrix similarity computation. Finally, the different size 2D honeycomb variable density cellular structures are designed and taken as the cases to verify the feasibility and effectiveness of proposed method.

Key words: local relative density mapping, matrix similarity, topology optimization, variable density cellular structure, voxelization

中图分类号:

TP391

赵芳垒, 敬石开, 刘晨燕. 基于局部相对密度映射的变密度多孔结构设计方法[J]. 机械工程学报, 2018, 54(19): 121-128.

ZHAO Fanglei, JING Shikai, LIU Chenyan. Variable Density Cellular Structure Design Method Base on Local Relative Density Mapping[J]. Journal of Mechanical Engineering, 2018, 54(19): 121-128.

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基于局部相对密度映射的变密度多孔结构设计方法

Variable Density Cellular Structure Design Method Base on Local Relative Density Mapping

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