A discontinuity analysis of generalized thermoelasticity theory with memory-dependent derivatives

2017 ◽  
Vol 228 (7) ◽  
pp. 2675-2689 ◽  
Author(s):  
Soumen Shaw ◽  
Basudeb Mukhopadhyay
Keyword(s):  
Generalized Thermoelasticity ◽  
Thermoelasticity Theory ◽  
With Memory

scholarly journals Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Mechanical Damage ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Temperature Parameter ◽  
Thermoelastic Solid ◽  
The One ◽  
Parameter Values ◽  
Two Temperature

AbstractThis work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

A novel magneto-thermoelasticity theory with memory-dependent derivative

2015 ◽  
Vol 29 (8) ◽  
pp. 1018-1031 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Ahmed S. El-Karamany ◽  
Alaa A. El-Bary
Keyword(s):  
Thermoelasticity Theory ◽  
With Memory

scholarly journals The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary ◽  
Eman A. N. Al-Lehaibi
Keyword(s):  
Fractional Order ◽  
Radial Distance ◽  
Generalized Thermoelasticity ◽  
Solid Sphere ◽  
Temperature Function ◽  
Thermoelasticity Theory ◽  
Mechanical Waves ◽  
Diagonalization Method ◽  
Temperature Parameter ◽  
Two Temperature

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress

2014 ◽  
Vol 6 (06) ◽  
pp. 783-796 ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
Ashraf M. Zenkour
Keyword(s):  
Initial Stress ◽  
Thick Plate ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Lower Surface ◽  
Thermoelasticity Problem ◽  
Mode Analysis ◽  
Thermoelasticity Theory ◽  
Phase Lags

AbstractIn this paper, the generalized thermoelasticity problem for an infinite fiber-reinforced transversely-isotropic thick plate subjected to initial stress is solved. The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading. The normal mode analysis is used to obtain the analytical expressions for the displacements, stresses and temperature distributions. The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress on the field quantities is shown graphically. The results due to the coupled thermoelasticity theory, Lord and Shulman’s theory, and Green and Naghdi’s theory have been derived as limiting cases. The graphs illustrated that the initial stress, the reinforcement and phase-lags have great effects on the distributions of the field quantities.

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