This paper provides a solution for a functionally graded hollow cylinder by using a novel numerical solution technique. The cylinder has an arbitrary elastic property along the radial direction. The cylinder is divided into N layers. The assumed Young's modulus in radial direction is approximated by the many power functions along layers. For an individual layer, two undetermined constants are involved in the elastic solution. Those undetermined coefficients can be evaluated from the continuation condition along interfaces of layers and the boundary conditions at the inner surface and outer surface of cylinder. After evaluating those coefficients, the displacement and the stress states in the cylinder are determined accordingly. This paper provides a universal method for solving the problem of FGM cylinder for the case of the arbitrary Young's modulus E(r) along the radial direction. Several numerical examples are presented in the paper. The obtained result shows that the FGMs property has a significant influence to the stress distribution.

本文通过一种新颖的数值求解技术为功能梯度空心圆柱提供了一种解决方案。圆柱体沿径向具有任意的弹性。圆柱体分为N层。沿径向假定的杨氏模量由沿层的许多幂函数近似。对于单个层，弹性解决方案中涉及两个不确定的常数。那些不确定的系数可以从沿着层界面的连续条件以及圆柱体的内表面和外表面的边界条件来评估。在评估了这些系数之后，即可确定圆柱体内的位移和应力状态。本文为解决沿径向任意杨氏模量E（r）的FGM圆柱体问题提供了一种通用方法。本文提供了几个数值示例。所得结果表明，FGMs的性质对应力分布有重要影响。