For the exact solution of the stress in the functionally graded (FG) cylindrical/spherical pressure vessel, this paper presents a unified form of the basic equations of the FG hollow cylinder/spherical shell by introducing parameter, and then, the axial/spherical symmetry mechanical problems of FG hollow shells are studied under three different boundary conditions, respectively. Assume that the Young's modulus of the material changes with thickness distribution of cylinder/shell in the form of power functions and the value of Poisson’s ratio is constant, the analytical solutions of the displacement and stress of the FG hollow cylindrical/spherical pressure vessel are derived under different boundary conditions. By comparing the analytical solutions of the FG hollow cylinder/spherical shell obtained in this paper with the existing classical theoretical solutions and numerical solutions, the correctness of the analytical solution given in this paper is verified. In the numerical discussion, the distributions of displacement, radial stress and circumferential stress of the FG hollow cylinder/spherical shell under different gradient parameters and different size conditions are given, respectively. Finally, based on the difference numerical method, the stress distribution of FG hollow cylinder/spherical shell with the Young's modulus and Poisson's ratio along thickness distribution in the form of power functions is analyzed numerically. The results show that gradient parameter and geometric size have a great influence on the mechanical response of FG structure under different boundary conditions.

为了精确求解功能梯度（FG）圆柱/球形压力容器中的应力，本文通过引入参数，然后给出轴向/球形对称性，给出了FG空心圆柱/球形壳体基本方程的统一形式。分别在三种不同的边界条件下研究了FG空心壳的力学问题。假设材料的杨氏模量以幂函数形式随圆柱/壳体厚度分布而变化，泊松比值恒定，则推导了FG空心圆柱/球形压力容器的位移和应力的解析解。在不同的边界条件下。通过将本文获得的FG空心圆柱/球壳的解析解与现有的经典理论解和数值解进行比较，验证了本文给出的解析解的正确性。在数值讨论中，分别给出了FG空心圆柱/球壳在不同梯度参数和不同尺寸条件下的位移，径向应力和周向应力的分布。最后，基于差分数值方法，以幂函数形式对沿杨氏模量和泊松比沿厚度分布的FG空心圆柱/球壳的应力分布进行了数值分析。