类方形蜂窝夹芯胞元尺寸的等效力学性能与优化
李响1,2，黄欢2，段宇2，殷圣地2
（1.三峡大学 石墨增材制造技术与装备湖北省工程研究中心，湖北 宜昌 443002；2.三峡大学 机械与动力学院，湖北 宜昌 443002）
摘要：为了提升类方形蜂窝等效力学性能，在推导了其尺寸参数与等效力学性能的函数后，将尺寸参数作为设计变量、等效力学性能为优化目标，建立了类方形蜂窝夹芯胞元优化数学模型，采用了多目标遗传算法进行优化设计。给出胞元尺寸单参数响应及多尺寸协同作用的响应分析并从多目标优化代表性解中选取到最优解。优化结果得到：当夹芯胞元尺寸参数l/t取114.3899、l/h取0.9598时，等效密度增加59.52%，y方向等效弹性模量减小了67.37%，但x方向等效弹性模量增大了109.77%，等效剪切模量增加了421.94%，类方形蜂窝夹芯的等效力学性能显著提升。研究结果对类方形蜂窝夹层结构的优化设计提供一定的依据和参考。
关键词：类方形蜂窝；等效力学性能；优化设计；胞元尺寸
中图分类号：O342 文献标志码：A doi：10.3969/j.issn.1006-0316.2023.09.001
文章编号：1006-0316 (2023) 09-0001-07
Equivalent Mechanical Properties and Optimization of Quasi-Square Honeycomb Sandwich Cell Size
LI Xiang1,2，HUANG Huan2，DUAN Yu2，YIN Shengdi2
( 1.Hubei Engineering Research Center for Graphite Additive Manufacturing Technology and Equipment, China Three Gorges University, Yichang 443002, China; 2.College of Mechanical and Power Engineering, China Three Gorges University, Yichang 443002, China )
Abstract：In order to improve the equivalent mechanical performances of quasi-square honeycombs, a mathematical model of cell optimization was established and a multi-objective genetic algorithm was used for the optimization design. With deduction of the function of dimension parameters and equivalent mechanical properties, the size parameters were taken as the design variables and the equivalent mechanical properties were taken as the optimization objectives, The optimized results show that when the l/t is 114.3899 and the l/t is 0.9598, the equivalent density rose by 59.52%, the y-direction equivalent elastic modulus decreased by 67.37%. In contrast, the equivalent elastic modulus in x-direction rose by 109.77% and the equivalent shear modulus rose by 421.94%. The equivalent mechanical performances of quasi-square honeycomb structure are significantly improved. The research results provide some basis and reference for the optimal design of honeycomb sandwich structures.
Key words：quasi-square honeycomb；equivalent mechanical performance；optimized design；cell size
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收稿日期：2022-12-26
基金项目：国家自然科学基金（51975325、51305232）；三峡大学石墨增材制造技术与装备湖北省工程研究中心开放基金（HRCGAM202108）
作者简介：李响（1979－），男，湖北黄梅人，博士，副教授、硕士生导师，主要研究方向为轻量化技术、结构优化设计、数值模拟技术、结构强度与可靠性等，E-mail：lixiangcfy@ctgu.edu.cn。
（1.三峡大学 石墨增材制造技术与装备湖北省工程研究中心，湖北 宜昌 443002；2.三峡大学 机械与动力学院，湖北 宜昌 443002）
摘要：为了提升类方形蜂窝等效力学性能，在推导了其尺寸参数与等效力学性能的函数后，将尺寸参数作为设计变量、等效力学性能为优化目标，建立了类方形蜂窝夹芯胞元优化数学模型，采用了多目标遗传算法进行优化设计。给出胞元尺寸单参数响应及多尺寸协同作用的响应分析并从多目标优化代表性解中选取到最优解。优化结果得到：当夹芯胞元尺寸参数l/t取114.3899、l/h取0.9598时，等效密度增加59.52%，y方向等效弹性模量减小了67.37%，但x方向等效弹性模量增大了109.77%，等效剪切模量增加了421.94%，类方形蜂窝夹芯的等效力学性能显著提升。研究结果对类方形蜂窝夹层结构的优化设计提供一定的依据和参考。
关键词：类方形蜂窝；等效力学性能；优化设计；胞元尺寸
中图分类号：O342 文献标志码：A doi：10.3969/j.issn.1006-0316.2023.09.001
文章编号：1006-0316 (2023) 09-0001-07
Equivalent Mechanical Properties and Optimization of Quasi-Square Honeycomb Sandwich Cell Size
LI Xiang1,2，HUANG Huan2，DUAN Yu2，YIN Shengdi2
( 1.Hubei Engineering Research Center for Graphite Additive Manufacturing Technology and Equipment, China Three Gorges University, Yichang 443002, China; 2.College of Mechanical and Power Engineering, China Three Gorges University, Yichang 443002, China )
Abstract：In order to improve the equivalent mechanical performances of quasi-square honeycombs, a mathematical model of cell optimization was established and a multi-objective genetic algorithm was used for the optimization design. With deduction of the function of dimension parameters and equivalent mechanical properties, the size parameters were taken as the design variables and the equivalent mechanical properties were taken as the optimization objectives, The optimized results show that when the l/t is 114.3899 and the l/t is 0.9598, the equivalent density rose by 59.52%, the y-direction equivalent elastic modulus decreased by 67.37%. In contrast, the equivalent elastic modulus in x-direction rose by 109.77% and the equivalent shear modulus rose by 421.94%. The equivalent mechanical performances of quasi-square honeycomb structure are significantly improved. The research results provide some basis and reference for the optimal design of honeycomb sandwich structures.
Key words：quasi-square honeycomb；equivalent mechanical performance；optimized design；cell size
———————————————
收稿日期：2022-12-26
基金项目：国家自然科学基金（51975325、51305232）；三峡大学石墨增材制造技术与装备湖北省工程研究中心开放基金（HRCGAM202108）
作者简介：李响（1979－），男，湖北黄梅人，博士，副教授、硕士生导师，主要研究方向为轻量化技术、结构优化设计、数值模拟技术、结构强度与可靠性等，E-mail：lixiangcfy@ctgu.edu.cn。
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