摘要
基于含7个自由度变量的改进Reddy型三阶剪切变形理论(third-order deformation theory,TSDT)假设,采用稳定移动最小二乘近似(stabilized moving least-square approximation,SMLS)的无网格法研究了功能梯度石墨烯增强复合材料(functionally graded graphene-reinforced composite,FG-GRC)板结构的静态线性弯曲和自振模态。通过Halpin-Tsai模型来估算材料的有效弹性模量,有效质量密度和泊松比由混合定律确定。利用最小势能原理和Hamition原理分别推导了FG-GRC板的线性弯曲和自振频率无网格控制方程。由于基于SMLS构造的形函数不满足克罗内克条件,故采用完全转换法处理本质边界条件。该研究首先介绍了基于TSDT下FG-GRC板的SMLS离散模型;随后通过与已有成果进行比较,检验了本文方法的收敛性及准确性;最后数值分析了石墨烯片(graphene platelets,GPLs)分布模式,质量分数、几何参数、总层数及边界条件等对FG-GRC板结构弯曲和模态的影响。
Based on the assumption of the improved Reddy type third-order deformation theory(TSDT)with seven degrees of freedom variables,the static linear bending and natural vibration modes of functionally graded graphene-reinforced composite(FG-GRC)plate structures were studied by using the meshless method of stabilized moving least-square approximation(SMLS).The effective Young’s modulus of the material was estimated by the Halpin-Tsai model,and the effective mass density and Poisson’s ratio were determined by the rule of mixture.The meshless governing equations for the linear bending deflection and natural frequency of FG-GRC plates were derived by using the principle of minimum potential energy and Hamilton principle,respectively.Since the shape function based on SMLS did not satisfy the Kronecker condition,the complete transformation method was used to deal with the essential boundary conditions.In the paper,firstly,the SMLS discrete model of the FG-GRC plate based on TSDT was introduced.Then,the convergence and accuracy of the method were tested by comparing with the existing results.Finally,the effects of the distribution mode of graphene platelets(GPLs),weight fraction,geometric parameters,total number of layers and boundary conditions on the bending deflection and vibration modes of FG-GRC plate structures were numerically analyzed.
作者
杨立军
陈孔
陈卫
YANG Lijun;CHEN Kong;CHEN Wei(Furong College,Hunan University of Arts and Science,Changde 415000,China;South Branch of China Construction Eighth Engineering Bureau Co.,Ltd.,Nanning 530004,China;School of Civil Engineering,University of South China,Hengyang 421001,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2024年第2期79-87,305,共10页
Journal of Vibration and Shock
基金
湖南省自然科学基金资助项目(2022JJ30423)
国家自然科学基金资助项目(12162004)。
作者简介
第一作者:杨立军,男,博士,教授,1976年生;通信作者:陈卫,男,博士,讲师,1991年生。
