Abstract
This study aims to develop an exact analytical solution for steady-state thermo-mechanical stress in a functionally graded (FG) thick-walled cylindrical vessel. The cylinder is subjected to combined rotational speed and internal pressures while the thermal load is with convective and radiative boundary conditions. The dimensionless governing equations and boundary conditions, represented as a quartic equation, are derived and solved using Ferrari's method. The temperature, displacement, and stress fields across the thick-walled cylindrical vessel are calculated by finding the roots of the quartic equation. In order to investigate the accuracy of the exact analytical solution, a numerical model is constructed based on a standard Galerkin discretization approach of the finite element method (FEM). The analytical solutions and the results obtained through FEM show a high level of agreement. Furthermore, the study analyzes the effects of material parameters on temperature, displacement, and stress fields. Displacement, temperature, and stress fields are presented in the form of dimensionless graphs along the radial direction. For the considered parametric studies, results revealed that parabolic grading is beneficial than conventional grading. This study reveals that for the thermal loading, the maximum temperature, displacement, and tangential stress decrease for the parabolic grading. A similar but lower value of temperature, displacement, and tangential stress is also observed in the case of thermomechanical loading. This study is expected to assist in the assessment of the reliability of load calculations and contribute to the overall durability of pressure vessels. The results obtained from this study can provide valuable insights into thermo-elasticity and the thermo-mechanical behavior of thick-walled cylindrical vessels and can aid in the design and optimization of such systems.