石墨烯折纸超材料梁结构的屈曲分析  

Buckling Analysis of Graphene Origami Metamaterial Beam

作　　者：王宇航 王爱文[1] 蒋鹏程 谢玉粉 WANG Yuhang;WANG Aiwen;JIANG Pengcheng;XIE Yufen(School of Science,Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《力学季刊》2024年第1期248-258,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12272058,11772063)。

摘　　要：石墨烯折纸超材料具有负泊松比特性,可以有效提升结构的抗屈曲性能,在航空航天等工程领域中有着广泛的应用潜力.本文以石墨烯折纸超材料梁为研究对象,基于虚功原理,根据欧拉梁理论和冯卡门非线性应变位移关系,建立了梁在面内载荷作用下发生屈曲行为的非线性控制方程;采用数值渐进方法计算出了石墨烯折纸超材料梁发生屈曲行为的临界载荷,通过与已发表文献结果进行对比,验证了本文理论和算法的正确性.最后分析了石墨烯折纸的分布、含量、折叠度和边界条件对超材料梁结构非线性屈曲行为的影响,结果表明两端固支边界下结构的屈曲临界载荷最大,在结构表层分布更多的石墨烯、石墨烯含量的增大都会使屈曲临界载荷增大,而折叠度的增大会导致临界载荷减小.Graphene origami metamaterial has characteristics of negative Poisson's ratio,which can effectively improve the buckling resistance of the structure,and has a wide range of application potentials in aerospace and other engineering fields.In this paper,the graphene origami metamaterial beam is taken as the research object.Based on the principle of virtual work,according to the Euler beam theory and von-Karman's nonlinear strain displacement relationship,the nonlinear governing equation of the beam's buckling behavior under the in-plane load is established.The critical load of the buckling behavior of graphene origami metamaterial beam is calculated using the asymptotic numerical method,and the correctness of the theory and the algorithm in this paper is verified by comparing with the results in the published literature.Finally,the influences of graphene origami distribution,content,folding degree and boundary conditions on the nonlinear buckling behavior of graphene origami metamaterial beam structure are analyzed.The results show that the buckling critical load of the structure is the largest under the fixed boundary condition at both ends.The buckling critical load increases with the increase of graphene and graphene content on the surface of the structure,while decreases with the increase of folding degree.

关 键 词：超材料 石墨烯增强复合材料 梁结构 非线性屈曲 数值渐进法 

分 类 号：TB34[一般工业技术—材料科学与工程]