碳纳米管增强型功能梯度板的屈曲预测

Buckling analysis of carbon nanotube-reinforced functionally graded composite plates

基于一种新的修正偶应力理论,建立了碳纳米管(CNTs)增强型功能梯度板(CNTs/FGP)的屈曲模型。基于最小势能原理和一阶剪切变形理论,推导了该种板模型的平衡微分方程和相应的边界条件,并以四边简支方板的屈曲问题为例,讨论了材料尺度参数、CNTs的体积分数及4种不同CNTs分布形式对CNTs/FGP临界屈曲载荷的影响。结果表明:采用本文模型预测的CNTs/FGP的临界屈曲载荷总是大于传统宏观理论的预测结果,两种理论结果间的差距随着板几何尺寸的减小而逐渐增大;CNTs体积分数的少量增加,即可使板的临界屈曲载荷有明显的提升;CNTs的不同分布形式对临界屈曲载荷有显著的影响,在工程设计中应予以关注。

A novel model for buckling analysis of carbon nanotube-reinforced functionally gradedplates（CNTs/FGP）was presented based on a re-modified couple stress theory.The equilibrium equations and relevant boundary conditions were derived from principle of minimum potential energy in conjunction with the first-order shear deformation theory.A simply supported CNTs/FGP was taken as illustrative example and analytically solved.The effects of material scale parameters,volume fraction and distributional patterns of the CNTs on the critical buckling load were investigated.The numerical results indicate that the critical buckling loads predicted by the present model are always higher than those by the classical macroscopic theory,and the differences of the two theories gradually increase with decreasing of the plate＇s geometric size;a small amount of CNTs can tangibly enhance the critical buckling load;the patterns of CNTs in matrix have conspicuous influences on the critical buckling load,which should be considered in engineering design.