基于MK和TSDT的功能梯度石墨烯增强复合材料板屈曲分析  

Buckling Analysis of Functionally Graded Graphene-Reinforced Plates Based on Moving Kriging and Third-Order Deformation Theory

作　　者：陈卫 方耀楚 彭林欣[2,3] Wei Chen;Yaochu Fang;Linxin Peng(School of Civil Engineering,University of South China,Hengyang,421001;School of Civil Engineering and Architecture,Guangxi University,Nanning,530004;Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education,Guangxi Key Laboratory of Disaster Prevention and Engineering Safety,Guangxi University,Nanning,530004)

机构地区：[1]南华大学土木工程学院,衡阳421001 [2]广西大学土木建筑工程学院,南宁530004 [3]广西防灾减灾与工程安全重点实验室,工程防灾与结构安全教育部重点实验室,南宁530004

出　　处：《固体力学学报》2024年第2期213-224,共12页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(12162004,11562001);南华大学博士科研启动基金项目(Y00043-13)资助。

摘　　要：针对功能梯度石墨烯增强复合材料(FG-GRC)板屈曲行为问题,提出一种含7个自由度变量改进Reddy型三阶剪切变形理论(TSDT)和移动克里金(MK)插值的无网格模型.该模型不但能避免无网格法中第二类边界条件难以施加的问题,且不需人工引入剪切修正因子,适用于薄/中厚/厚板问题,同时具有较高的计算精度.通过Halpin-Tsai模型来预测FG-GRC板的有效杨氏模量,并根据混合定律来确定其有效泊松比.利用最小势能原理推导了含7个未知量FG-GRC板屈曲的无网格控制方程.通过与文献结果对比验证了方法的收敛性及有效性.数值结果表明:当FG-GRC板的总层数NL小于10~15时,FG-O和FG-X型的FG-GRC板临界屈曲荷载变化率较为剧烈,说明该阶段相较于环氧树脂板,GPLs增强板的刚度降低(或增加)较快;当FG-GRC板的总层数NL>10~15时,临界屈曲荷载变化率较为平缓;随着GPLs的长厚比l_(GPL)/hGPL增加到1000左右,FG-GRC板临界屈曲荷载急剧增加.当GPLs的长厚比l_(GPL)/hGPL增加到2000以上时,FG-GRC板临界屈曲荷载趋向于稳定且GPLs的长宽比l_(GPL)/wGPL和长厚比l_(GPL)/hGPL对FG-GRC板临界屈曲荷载影响不再明显.This paper proposed a new meshless model to solve the buckling behavior problem of functionally graded graphene-reinforced composite(FG-GRC)plates.The model is based on an improved Reddy-type third-order shear deformation theory(TSDT)with seven degrees of freedom and a moving Kriging(MK)interpolation method,which can avoid the problem of difficult implementation of the second type boundary conditions in meshless methods and eliminate the need for artificial introduction of shear correction factors.The model is applicable to thin/medium/thick plate problems and has high computational accuracy.The Halpin-Tsai model is used to predict the effective Young's modulus of the FG-GRC plate,and the effective Poisson's ratio are determined by the mixture law.The meshless govern equation for buckling of the FG-GRC plate with seven unknowns are derived based on the principle of minimum potential energy.The convergence and effectiveness of the proposed method are verified by comparing with literature results.The numerical results show that the critical buckling load of the epoxy pure plate is smaller than that of the FG-GRC plate,and increases with the weight fraction of graphene platelets(gGPL).The reinforcement effects of the three GPL distribution patterns are in the order of FG-X>UD>FG-O.When the total number of layers(NL)of the FG-GRC plate is less than 10-15,the critical buckling load of the FG-O and FG-X type plates changes more drastically than that of the epoxy pure plate,indicating that the stiffness of the graphene-reinforced plate decreases(or increases)rapidly compared to the epoxy pure plate in this stage.When NL>10-15,the change rate of the critical buckling load of the FG-GRC plate becomes smoother.The critical buckling load of the FG-GRC plate increases sharply when the length-thickness ratio of the GPLs reaches around 1000.When the length-thickness ratio of GPLs exceeds 2000,the critical buckling load of the FG-GRC plate tends to be stable,and the length-width ratio and length-thickness ratio of the GPLs have

关 键 词：功能梯度石墨烯增强复合材料板 改进Reddy型三阶剪切变形理论 移动克里金 临界屈曲荷载 

分 类 号：TB332[一般工业技术—材料科学与工程]