柔性支撑上FGM矩形薄板热屈曲的封闭形式解

Closed form solution for thermal buckling of rectangular FGM thin plates with flexible support

针对典型的热防护组合结构建立物理模型,基于经典薄板理论(CPT),选取中性面为分析平面,推导出柔性支撑上FGM矩形薄板热屈曲方程。利用分离变量法得到了柔性支撑上FGM矩形薄板热屈曲问题的封闭形式解,该方法不仅适用于对边简支情况也适用于四边固支情况。分别对均匀升温、线性升温和非线性升温三种温度场的临界屈曲热载荷进行了计算,与已有文献结果对比验证了本文方法以及结果的正确性,同时进行了数值分析并给出结论。

This article presents closed form solutions for thermal buckling of FGM rectangular thin plates with flexible support. A neutral surface is employed to eliminate the stretching-bending coupling in functionally graded plates. Based on CPT, the equilibrium equations of FGM plate with flexible support in thermal environment are derived. The separation-of-variables method is adopted to obtain the exact solutions for thermal buckling problems of FGM rectangular thin plates with simply supported boundary condition and clamped boundary condition. The buckling of FGM plates under three types of thermal loads is analyzed. The present formulations and solutions are validated by comprehensive comparisons with results in literature.