Time-dependent thermo-elastic creep response of rotating thick cylindrical shells made of axially functionally graded materials based on the TSDT

Abstract

This paper presents an analytical study on the time-dependent thermo-mechanical creep behavior of rotating thick cylindrical shells made of functionally graded materials (FGMs) with axial gradation. These structures are widely used in aerospace, nuclear, pressure vessels, and mechanical systems subjected to extreme thermal and mechanical environments where creep significantly affects long-term performance. Notably, the creep behavior of FGMs with axial variation has not been previously investigated. The third-order shear deformation theory (TSDT) is employed to model the structure, providing greater accuracy than classical and first-order shear deformation theory (FSDT), especially for thick shells. To the best of the authors' knowledge, TSDT has not been applied to analyze creep behavior before, marking a significant novelty of this work. Except for Poisson's ratio, all thermal and mechanical characteristics of the material vary gradually along the cylinder's axis based on a power-law model. The governing equations are derived using the principle of minimum total potential energy, resulting in a system of variable-coefficient nonhomogeneous differential equations. These equations are solved analytically via a multi-layered method (MLM), which transforms them into homogeneous equations with constant coefficients in each layer, enhancing accuracy over numerical or approximate methods. The creep behavior is modeled using Norton's law, and an iterative procedure is adopted to obtain time-dependent stress and displacement distributions. The analysis includes the effects of axial gradation, temperature gradients, internal pressure, and rotational forces. Results are validated against the finite element method (FEM), showing excellent agreement.