温度梯度下功能梯度材料圆柱壳的热屈曲

本文采用能量法研究了不同温度梯度下功能梯度材料圆柱壳的热屈曲行为。屈曲临界条件由里兹法得到。在临界条件中，由于材料属性和温度的耦合效应，临界温升通过迭代算法求得。文中讨论了两种温度梯度形式以及物性温度相关性对临界温升的影响。数值结果表明：功能梯度材料的组分参数只在一定小范围内对临界温升有显著影响；相比之下，结构尺寸参数的影响更大；在功能梯度材料圆柱壳热屈曲分析中考虑物性温度相关性是十分必要的，否则将大大地高估临界温升；若采用抛物型温度场来代替实际的热传导温度场，临界温升在陶瓷含量较多且壳厚较小的情况下，将可能被低估，而在金属含量较多且壳厚较大的情况下，却可能被高估。

Thermal Buckling of Functionally Graded Cylindrical Shells Subjected to Temperature Gradients

Thermal buckling behaviors of functionally graded cylindrical shells subjected to temperature gradients through the shell thickness are investigated by using the energy method. The Ritz method is applied to obtain the critical condition, which is then solved by an iterative algorithm due to coupling effects between the material properties and the temperature field. The effects of two kinds of temperature gradients and temperature-dependent material properties are carefully discussed in this paper. Numerical results show the critical temperature rise is only markedly affected by the inhomogeneous parameter of functionally graded materials in a small scope. The effect of dimension of structure is greater than that of the inhomogeneous parameter. It is essential to consider the temperature-dependent properties in thermal buckling analysis of functionally graded cylindrical shells, or the critical temperature rise would be greatly overestimated. If the assumed quadratic distribution is used to approximate the actual steady one-dimensional thermal conduction, the critical temperature rise would tend to be underestimated in the case of a ceram-richer, thinner shell, while, in the case of a metal-richer, thicker shell, it would be overestimated.