The present article deals with the analysis of thermal-bending stresses in a heated thin annular sector plate with simply supported boundary condition under transient temperature distribution using Berger’s approximate methods. The sectional heat supply is on the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the solution of heat conduction is obtained by the classical method. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using thermally induce resultant moment and resultant forces. The numerical calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the results for temperature, deflection, resultant bending moments and thermal stresses have been illustrated graphically with the help of MATHEMATICA software. تفاصيل المقالة

An analytical framework is developed for the thermoelastic analysis of annular sector plate whose boundaries are subjected to elastic reactions. The exact expression for transient heat conduction with internal heat sources is obtained using a classical method. The fourth-order differential equation for the thermally induced deflection is obtained by developing a new integral transformation in accordance with the simply supported elastic supports that are subjected to elastic reactions. Here it is supposed that the movement of the boundaries is limited by an elastic reaction, that is, (a) shearing stress is proportional to the displacement, and (b) the reaction moment is proportional to the rate of change of displacement with respect to the radius. Finally, the maximum thermal stresses distributed linearly over the thickness of the plate are obtained in terms of resultant bending momentum per unit width. The calculation is obtained for the steel, aluminium and copper material plates using Bessel's function can be expressed in infinite series form, and the results are depicted using a few graphs. تفاصيل المقالة

A fractional Cattaneo model from the generalized Cattaneo model with two fractional derivatives of different orders is considered for studying the thermoelastic response for a multilayer elliptic ring membrane with source function. The solution is obtained by applying an integral transform technique analogous to Vodicka's approach considering series expansion functions in terms of an eigenfunction to the generalized fractional Cattaneo-type heat conduction equation within an elliptic coordinates system. The analytical expressions of displacement and stress components employing Airy's stress function approach are investigated. The results are obtained as a series solution in terms of Mathieu functions and hold convergence test. The effects of fractional parameters on the temperature fields and their thermal stresses are also discussed. The findings are depicted graphically for different kinds of surface temperature gradients, and it is distinguished that the higher the fractional-order parameter, the higher the thermal response. Lastly, the generalized theory of thermoelasticity predicts an instantaneous response, but the fractional theory, which is currently under consideration, predicts a delayed response to physical stimuli, which is something that can be seen occurring in nature. This delayed response can be explained by the fact that fractional theories are currently being considered. This gives credibility to the motivation behind this topic of study in the research. تفاصيل المقالة

In this study, the analysis focuses on a transient thermoelastic problem in an isotropic homogeneous elastic plate that is exposed to heat loading within the framework of the fractional-order theory. The sectional heat supply is applied on both the front edge and the farthest edge of the rectangular plate. The integral transformation was considered as a means to solve the main governing equations. The Mittag-Leffler function is utilized to express the analytical solution for temperature change, displacement, and stress response. The investigation also encompasses the study of thermoelastic behaviors in a plate featuring a central crack. The stress intensity factors at the fracture tip are determined numerically using the weight function method in this proposed solution. The findings are depicted using numerical computations, considering the material as a media, and visually represented in graphical form. The findings of this investigation indicate that the utilization of the theory of generalized thermoelasticity with fractional order heat transfer provides a more precise depiction of the behavior shown by the constituent particles comprising an elastic body, in comparison to the theory of generalized thermoelasticity with integer order.

تفاصيل المقالة