功能梯度椭圆柱壳的热力耦合屈曲分析

Coupled Thermo-Mechanical Buckling Analysis of Functionally Graded Elliptical Cylindrical Shells

假设功能梯度材料中陶瓷组分体积分率服从幂率分布,材料属性沿厚度方向连续变化且与温度相关,采用经典的Donnell壳体理论和伽辽金原理研究了功能梯度材料椭圆柱壳的热力耦合屈曲问题.推导了功能梯度椭圆柱壳的屈曲控制方程及屈曲临界温度的解析表达式,分析了均匀分布、线性分布及非线性分布(考虑热传导效应)的温升环境对材料物性的温度相关性的影响,以及屈曲临界温度随截面离心率、材料组分参数的变化规律.结果表明:材料物性温度相关性对屈曲临界温度的影响较大,若将其忽略,可能导致屈曲临界温度被高估15%;在考虑物性温度相关性的情况下,均匀温升作为温度公式的简化,可能导致对真实结构屈曲临界温度的低估;屈曲临界温度随着椭圆截面离心率、径厚比及组分参数的增大而减小.

In the assumption that the volume fraction of ceramic constituents in functionally graded material sobeys the power law distribution and that the material properties are temperature-dependent and graded in thickness direc-tion ,the coupled thermo-mechanical buckling of functionally graded elliptical cylindrical shells is investigated in light of the classical Donnell shell theory and Galerkin^ principle. Firstly, the buckling governing equations of functionally graded elliptical cylindrical shells and the critical buckling temperature are analytically derived. Then, the temperature-dependent physical properties of the materials are analyzed respectively under uniform, linear and nonlinear （considering heat conduction effect） temperature rise. Finally, the variation of critical buckling tempera-ture with the eccentricity of section and with the parameters of material components is explored. The results show that, as the temperature-dependent physical properties affect the critical buckling temperature greatly, it should be taken into consideration in the thermal buckling analysis of functionally graded elliptical cylindrical shells, other-wise the critical buckling temperature will be overestimated by 15% ; when considering the temperature- dependent- material properties, the uniform temperature rise as a simplified form of temperature may lead to an underestimation of the critical buckling temperature of the real structure; and that the critical buckling temperature decreases with the increase of ellipse section7 s eccentricity, radius- to-thickness ratio and parameters of material components.