工程科学学报，第39卷，第9期：1386-1395,2017年9月 Chinese Journal of Engineering,Vol.39,No.9:1386-1395,September 2017 D0l:10.13374/j.issn2095-9389.2017.09.012;htp:/journals..usth.edu.cn 基于渐进变分法的蛋盒型结构等效刚度分析及优化 臧 勇，王远，秦勤区，管奔 北京科技大学机械工程学院，北京100083 ☒通信作者，E-mail:qinqin@me.usth.cdu.cn 摘要对蛋盒型结构的等效刚度特性进行了分析并实现了蛋盒型结构参数的优化设计.首先以蛋盒型结构的单胞为研究 对象，基于渐进变分法，得到了蛋盒型结构等效刚度特性的数值计算方法.随后用该方法计算蛋盒型结构不同参数情况下的 等效刚度特性，并以结构参数为自变量，等效刚度特性为因变量进行拟合.最后应用拟合公式在限定泊松比或等效刚度的情 况下，分别以最大化结构的屈曲载荷和最大化单位质量吸能能力的优化为例，对蛋盒型结构参数进行了量纲为一的优化设 计.计算结果表明：蛋盒型结构拉伸刚度降低，弯曲刚度升高：蛋盒型结构的刚度特性与结构参数之间呈现非线性的特点，结 构表现出负泊松比的特性：在给定优化目标和限定条件时应用拟合公式可以快速实现蛋盒型结构参数的主动优化设计. 关键词蛋盒型结构：渐进变分法：等效刚度：结构优化 分类号TB383 Equivalent stiffness and optimized design of egg-box structure based on variational as- ymptotic method ZANG Yong,WANG Yuan,QIN Qin,GUAN Ben School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:gingin@me.ustb.edu.cn ABSTRACT The equivalent stiffness of the egg-box structure was investigated to achieve structural optimization of the structure pa- rameters.A unit cell of the egg-box structure was studied using the variational asymptotic method to obtain a numerical calculation method for equivalent stiffness of the whole egg-box structure.This numerical calculation method was then used to analyze the equiva- lent stiffness of the egg-box structure with different structural parameters.A formula for equivalent stiffness characteristics was then fit- ted,and the structural parameters were treated as independent variables.Finally,the fitted formula was used to optimize the dimen- sionless structural parameters to obtain maximum buckling load and maximum energy absorbed per unit weight when Poisson's ratio or equivalent stiffness was restricted.Results show that the tensile stiffness of the egg-box structure is reduced,but the bending stiffness is increased.In addition,there is a nonlinear relationship between stiffness and structural parameters,and the structure exhibits a negative Poisson's ratio.Furthermore,active parameters optimization design of the egg-box structure can be easily achieved with the fitted formula. KEY WORDS egg-box structure;variational asymptotic method;equivalent stiffness;structural optimization 蛋盒型结构是一种具有较高的吸能质量比，较好 是金属薄板、聚合物板或复合材料板等，其结构经过简 的抗弯曲扭转性能，较好的高温稳定性等特点的轻质 单的冷冲压或热冲压即可得到，已经在汽车、船舶行业 结构).同时该种结构易制造易回收，其原材料可以 得到应用 收稿日期：2017-02-22 基金项目：中央高校基本科研业务费资助项目(FF-TP-16-010A3):工信部2016年智能制造综合标准化与新模式应用项目工程科学学报,第 39 卷,第 9 期:1386鄄鄄1395,2017 年 9 月 Chinese Journal of Engineering, Vol. 39, No. 9: 1386鄄鄄1395, September 2017 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2017. 09. 012; http: / / journals. ustb. edu. cn 基于渐进变分法的蛋盒型结构等效刚度分析及优化 臧 勇, 王 远, 秦 勤苣 , 管 奔 北京科技大学机械工程学院, 北京 100083 苣通信作者, E鄄mail: qinqin@ me. ustb. edu. cn 摘 要 对蛋盒型结构的等效刚度特性进行了分析并实现了蛋盒型结构参数的优化设计. 首先以蛋盒型结构的单胞为研究 对象,基于渐进变分法,得到了蛋盒型结构等效刚度特性的数值计算方法. 随后用该方法计算蛋盒型结构不同参数情况下的 等效刚度特性,并以结构参数为自变量,等效刚度特性为因变量进行拟合. 最后应用拟合公式在限定泊松比或等效刚度的情 况下,分别以最大化结构的屈曲载荷和最大化单位质量吸能能力的优化为例,对蛋盒型结构参数进行了量纲为一的优化设 计. 计算结果表明:蛋盒型结构拉伸刚度降低,弯曲刚度升高;蛋盒型结构的刚度特性与结构参数之间呈现非线性的特点,结 构表现出负泊松比的特性;在给定优化目标和限定条件时应用拟合公式可以快速实现蛋盒型结构参数的主动优化设计. 关键词 蛋盒型结构; 渐进变分法; 等效刚度; 结构优化 分类号 TB383 Equivalent stiffness and optimized design of egg鄄box structure based on variational as鄄 ymptotic method ZANG Yong, WANG Yuan, QIN Qin 苣 , GUAN Ben School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China 苣Corresponding author, E鄄mail: qinqin@ me. ustb. edu. cn ABSTRACT The equivalent stiffness of the egg鄄box structure was investigated to achieve structural optimization of the structure pa鄄 rameters. A unit cell of the egg鄄box structure was studied using the variational asymptotic method to obtain a numerical calculation method for equivalent stiffness of the whole egg鄄box structure. This numerical calculation method was then used to analyze the equiva鄄 lent stiffness of the egg鄄box structure with different structural parameters. A formula for equivalent stiffness characteristics was then fit鄄 ted, and the structural parameters were treated as independent variables. Finally, the fitted formula was used to optimize the dimen鄄 sionless structural parameters to obtain maximum buckling load and maximum energy absorbed per unit weight when Poisson爷s ratio or equivalent stiffness was restricted. Results show that the tensile stiffness of the egg鄄box structure is reduced, but the bending stiffness is increased. In addition, there is a nonlinear relationship between stiffness and structural parameters, and the structure exhibits a negative Poisson爷s ratio. Furthermore, active parameters optimization design of the egg鄄box structure can be easily achieved with the fitted formula. KEY WORDS egg鄄box structure; variational asymptotic method; equivalent stiffness; structural optimization 收稿日期: 2017鄄鄄02鄄鄄22 基金项目: 中央高校基本科研业务费资助项目(FRF鄄鄄TP鄄鄄16鄄鄄010A3);工信部 2016 年智能制造综合标准化与新模式应用项目 蛋盒型结构是一种具有较高的吸能质量比,较好 的抗弯曲扭转性能,较好的高温稳定性等特点的轻质 结构[1] . 同时该种结构易制造易回收,其原材料可以 是金属薄板、聚合物板或复合材料板等,其结构经过简 单的冷冲压或热冲压即可得到,已经在汽车、船舶行业 得到应用