Analysis of elastic stresses for a composite disk under the parabolic distribution of temperature using the rayleigh-ritz method with trigonometric ritz functions

This study presents a comprehensive analysis of the elastic stresses in a composite disk subjected to a parabolic temperature distribution. The disk, reinforced with steel fibers, is modeled as a thermo-elastic composite material. The Rayleigh-Ritz method, a well-established numerical technique for solving boundary value problems, is employed to derive analytical solutions for the radial and tangential stresses. The method leverages the principle of minimum potential energy to approximate the displacement fields using Trigonometric Ritz Functions, which are then used to compute the stress components. The parabolic temperature distribution introduces a non-uniform thermal load across the disk, significantly influencing the stress distribution. The study investigates how the temperature effect, inherent in the composite material, interacts with the thermal variations, leading to complex stress patterns. By varying the temperature parameters, the analysis reveals the sensitivity of the stress components to thermal gradients. Comparative analyses are conducted for different temperature profiles, highlighting the critical regions of stress concentration. The results provide valuable insights into the behavior of thermo-elastic composites under non-uniform thermal conditions, offering a robust analytical framework for future research and practical applications in engineering design. This study underscores the importance of considering both thermal and Trigonometric Ritz Functions in the design and analysis of composite structures subjected to varying temperature loads.