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

DOI：

 作者 单位 E-mail 邓阳 湘潭大学 dyingfight@163.com 尹硕辉 湘潭大学机械工程学院 yinsh2016@163.com 赵子衡 湘潭大学机械工程学院

基于修正偶应力理论和Kirchhoff板理论，采用等几何有限元法建立了功能梯度微板热力耦合屈曲模型。功能梯度材料的物性参数采用幂函数模型表示，微结构的尺度效应现象由只包含一个材料尺度参数的修正偶应力理论来描述，采用等几何有限元法能满足修正偶应力理论对高阶连续性的要求。本文基于虚功原理推导了功能梯度微板的热力耦合屈曲等几何有限元方程。数值结果与解析结果对比，验证了该模型的正确性。通过对功能梯度微板热力耦合屈曲的典型算例分析，讨论了材料尺度参数、板的边长比对功能梯度微板稳定性的影响。结果表明：本文模型预测的功能梯度微板临界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；材料尺度参数和边长比的增加可提高功能梯度微板的稳定性；随着临界屈曲力的增加，临界屈曲热载荷呈线性递减，同时，增加临界屈曲热载荷也会线性降低临界屈曲力。说明在设计微结构时，需要考虑热力耦合作用的影响。

Based on the modified couple stress theory (MCST) in conjunction with the Kirchhoff plate theory, a model for thermal-mechanical buckling analysis of functionally graded（FG）micro plates was presented using isogeometric finite element method. The power law method was used to indicate the FG material properties, the size effect was captured by the MCST, which contains only one material length scale parameter, the requirement of the MCST for high-order continuity was satisfied by the isogeometric finite element method, the principle of virtual work was employed to drive isogeometric finite element equations of the thermal-mechanical buckling of FG micro plates. Numerical results are compared with exact solutions to confirm the accuracy of the proposed method. In order to investigate the effects of the material scale parameter and the aspect ratio on the thermal-mechanical stability of FG micro plates, a typical FG micro plates under thermal-mechanical loads was taken as illustrative example. The results reveal that the critical buckling predicted by present method is lager than that of the classical one, which means the size effect can be captured; the increment of the material scale parameter and the aspect radio enhance the stability of micro plates; with the increase of the critical mechanical load, the critical thermal load is decreasing linearly. Meanwhile, the increase of the critical thermal load also reduce linearly the critical mechanical load, which indicate thermal-mechanical coupled effect should be considered in design of micro-structure.
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