基于等几何有限元法的功能梯度微板热力耦合屈曲预测

Thermal-mechanical buckling analysis of functionally graded micro plates using isogeometric finite element method

基于修正偶应力理论和Kirchhoff板理论,建立了功能梯度微板热力耦合屈曲等几何有限元模型。该模型仅包含一个材料尺度参数,能够描述尺度效应现象,且满足修正偶应力理论的高阶连续性要求。基于虚功原理推导了功能梯度微板热力耦合屈曲等几何有限元方程。通过对板的典型算例分析,讨论了材料尺度参数、边长比及梯度指数对板稳定性的影响。结果表明,本文模型预测的屈曲载荷总是大于宏观理论的结果,即捕捉到了尺度效应现象;随着临界屈曲力的增加,临界屈曲热载荷线性减少;此外,边长比和梯度指数也对微板的稳定性产生一定影响。

Based on the modified couple stress theory(MCST)in conjunction with the Kirchhoff plate theory,an isogeometric finite element model for thermal-mechanical buckling analysis of functionally graded(FG)micro plates was presented.This model only had one material length scale parameter,which was able to capture the size effect,and satisfied the requirement of the MCST for high-order continuity.The principle of virtual work was employed to derive isogeometric finite element equations of the thermal-mechanical buckling of FG micro plates.In order to investigate the effects of the material scale parameter,the aspect ratio and the gradient index on the thermal-mechanical stability of FG micro plates,a typical FG micro plates under thermal-mechanical loads was taken as an illustrative example.The results reveal that the critical buckling predicted by the present method is larger than that of the classical one,which means the size effect can be captured;with the increase of the critical mechanical load,the critical thermal load is decreasing linearly.Meanwhile,the aspect radio and the gradient index also have some effects on the stability of micro plates.