A practical approach is implemented for thermal stresses in an axisymmetric thin annular fin, made of functionally graded material. All material properties of the annular fin are assumed to be graded along the fin radius as a power-law function. A linear differential equation is derived to be the governing equation. Analytical solution of such equations except for simple grading functions is difficult or maybe not possible to implement for each parameter, so the numerical approach becomes inevitable. The novelty of the present study is to introduce the effects of mechanical and thermal properties on the thermal stress distribution of functionally graded annular fin with the help of a complementary function method (CFM). The complementary functions method will be incorporated into the analysis to convert the problem to an initial value problem, which can be easily solved by, for instance, Runge−Kutta methods with great accuracy. The results are validated for isotropic and homogeneous annular fin.

中文翻译：

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功能梯度环形翅片热应力的实用方法

在功能对称材料制成的轴对称薄环形翅片中实施了一种热应力实用方法。假定环形翅片的所有材料特性均沿翅片半径分级，作为幂律函数。推导线性微分方程作为控制方程。除了简单的等级函数之外，此类方程的解析解很难或不可能针对每个参数实施，因此数值方法变得不可避免。本研究的新颖性是借助互补函数方法（CFM）来介绍机械性能和热性能对功能梯度环形鳍片热应力分布的影响。互补函数法将被纳入分析，以将问题转换为初始值问题，这可以很容易地通过例如Runge-Kutta方法很精确地解决。对于各向同性和均质的环形翅片，结果得到了验证。