首页|基于MK和TSDT的功能梯度石墨烯增强复合材料板屈曲分析

基于MK和TSDT的功能梯度石墨烯增强复合材料板屈曲分析

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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lGPL/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lGPL/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lGPL/wGPL和长厚比lGPL/hGPL对FG-GRC板临界屈曲荷载影响不再明显.
Buckling Analysis of Functionally Graded Graphene-reinforced Plates Based on Moving Kriging and Third-order Deformation Theory
The emergence of graphene nanoplatelets(GPLs)has enabled the development of light-weight and high-strength plates,making it a prominent area of research in science and engineering.There-fore,it is essential to study the buckling performance of functionally graded graphene-reinforced composite(FG-GRC)plates.This paper presents a new meshless model to solve the buckling behavior problem of FG-GRC plates.The model is based on an improved Reddy-type third-order shear deformation theory(TS-DT)with seven degrees of freedom and a moving Kriging(MK)interpolation method,which can overcome the challenge of implementing the second-type boundary conditions in meshless methods and eliminate the need for 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 is determined using the mixture law.The meshless governing equation for the buckling of the FG-GRC plate with seven unknowns is derived based on the principle of minimum potential energy.The convergence and effectiveness of the proposed method are veri-fied by comparing it with literature results.The numerical results demonstrate that 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-type 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 in this stage,as opposed to the epoxy pure plate.However,when NL exceeds 10-15,the change rate of the critical buckling load for the FG-GRC plate be-comes smoother.Furthermore,the critical buckling load of the FG-GRC plate increases sharply when the length-thickness ratio of the GPLs reaches around 1000.Once the length-thickness ratio of GPLs surpasses 2000,the critical buckling load of the FG-GRC plate tends to stabilize,and the length-width ratio and length-thickness ratio of the GPLs have no significant effect on it.Overall,the research findings of this study not only contribute to the understanding of FG-GRC plates but also offer practical and insightful rec-ommendations for their design and theoretical research.

functionally graded graphene-reinforced composite platesimproved Reddy-type third-or-der shear deformation theorymoving Krigingcritical buckling load

陈卫、方耀楚、彭林欣

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南华大学土木工程学院,衡阳,421001

广西大学土木建筑工程学院,南宁,530004

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

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

国家自然科学基金国家自然科学基金南华大学博士科研启动基金

1216200411562001Y00043-13

2024

10.19636/j.cnki.cjsm42-1250/o3.2023.052

固体力学学报
中国力学学会

固体力学学报

CSTPCD北大核心
影响因子：0.605
ISSN：0254-7805
年,卷(期)：2024.45(2)
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