Analysis of elastic stresses and thermal creep effect for a composite disk under the parabolic distribution of temperature using the Rayleigh-Ritz method with trigonometric Ritz functions

Abstract

This research provides a detailed examination of the thermal creep effect on elastic stresses in a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is treated as a thermo-elastic composite material. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for the radial and tangential stresses. This method employs the principle of minimum potential energy to approximate displacement fields using Trigonometric Ritz Functions, which are subsequently applied to calculate the stress components. The parabolic temperature distribution imparts a non-uniform thermal load across the disk, significantly affecting the stress distribution. The study explores how the thermal creep effect, intrinsic to the composite material, interacts with thermal variations, resulting in intricate stress patterns. By adjusting temperature parameters, the analysis demonstrates the sensitivity of stress components to thermal gradients. Comparative assessments are performed for various temperature profiles, identifying critical areas of stress concentration. The findings offer significant insights into the behavior of thermo-elastic composites under non-uniform thermal conditions, providing a robust analytical foundation for future research and engineering applications. This research emphasizes the necessity of considering both thermal creep effects and Trigonometric Ritz Functions in the design and analysis of composite structures subjected to varying temperature loads.