Probabilistic Thermo-Viscoelastic Analysis Of A Composite Disk Under Parabolic Temperature Distribution Using The Rayleigh-Ritz Method

Abstarct: This investigation centers on the stochastic thermo-viscoelastic response of a composite disk subjected to a parabolic temperature gradient. The analysis leverages the Rayleigh-Ritz method, coupled with trigonometric Ritz functions, to model the time-dependent dynamic behavior of the disk. A core objective is to elucidate how probabilistic variations in temperature and viscoelastic material attributes affect the radial and tangential stresses and strains within the disk. The probabilistic thermo-viscoelastic problem is formulated by considering the temporal evolution of stresses and strains, incorporating both thermal expansion and viscoelastic relaxation phenomena. The radial and tangential stresses are expressed as time-varying functions, governed by their respective relaxation moduli. These moduli capture the material's viscoelastic nature, while randomized thermal expansion coefficients represent temperature-induced strain deviations. The parabolic temperature profile generates a spatially inhomogeneous thermal loading, which is integrated within the thermo-viscoelastic formulation. The Rayleigh-Ritz method facilitates the discretization of the problem, using trigonometric Ritz functions to describe the spatial variation of stresses and strains. This framework permits efficient computation of the disk’s dynamic behavior, accounting for the material’s anisotropic and viscoelastic properties. The findings emphasize the interplay between thermal fluctuations and viscoelastic dissipation in shaping the stress and strain distributions. The non-uniform temperature profile generates spatially varying thermal expansion, which couples with the viscoelastic relaxation mechanisms to produce intricate stress patterns. This probabilistic analysis yields insights into the temporal evolution of stresses and strains, providing a robust understanding of the thermo-viscoelastic behavior of the composite disk under uncertain thermal loading conditions.