Theory of Generalized Micropolar Thermoelasticity and an Axisymmetric Half-Space Problem

Sherief, Hany H.; Hamza, Farid A.; El-Sayed, Amany M.

doi:10.1080/01495730590916641

Cited by 78 publications

(33 citation statements)

References 24 publications

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“…Some problems for a penny shaped crack and a mode I crack were solved by Sherief and El-Maghraby [6,7]. This theory was extended by Sherief et al [8] to micropolar media. Anwar and Sherief [9] studied a problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials.…”

Section: Introductionmentioning

confidence: 98%

Fractional model of thermoelasticity for a half‐space overlaid by a thick layer

El-Latief

Khader

2014

Z Angew Math Mech

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In this work, we apply the fractional order theory of thermoelasticity to a 1D problem for a half-space overlaid by a thick layer of a different material. The upper surface of the layer is taken to be traction free and is subjected to a constant thermal shock. There are no body forces or heat sources affecting the medium. Laplace transform techniques are used to eliminate the time variable t. The solution in the transformed domain is obtained by using a direct approach. The inverse Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques.The predictions of the fractional order theory are discussed and compared with those for the generalized theory of thermoelasticity. We also study the effect of the fractional derivative parameters of the two media on the behavior of the solution. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

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Section: Introductionmentioning

confidence: 98%

Fractional model of thermoelasticity for a half‐space overlaid by a thick layer

El-Latief

Khader

2014

Z Angew Math Mech

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“…(14) By eliminating η between (9) and (14) and using (10) we get the equation of heat conduction for the linear theory as follows k∇ 2 θ = ∂ ∂t…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The generalized theory of micropolar thermoelasticity, which admits the second sound effect, was established by Boschi and Iesan [13], Sherief et al [14] introduced another model and proved the uniqueness theorem and solved an axisymmetric thermal shock problem. El-Karamany and Ezzat [15] The foundations of magneto-elasticity were presented by Knopoff [16], Chadwick [17] and developed by Kaliski and Petykiewicz [18].…”

Section: Introductionmentioning

confidence: 99%

Micropolar generalized magneto-thermoelasticity with modified Ohm's and Fourier's laws

Ezzat

Awad

2009

Journal of Mathematical Analysis and Applications

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In this work, we introduce the modified Ohm's law, including the temperature gradient and charge density effects, and the generalized Fourier's law, including the current density effect, to the equations of the linear theory of micropolar generalized magnetothermoelasticity, allowing the second sound effects. A normal mode analysis is applied to obtain the exact formulas of temperature, displacement, micro-rotation, stresses, couple stresses, electric field, magnetic field and current density. Application is employed to our problem to get the solution in the complete form. The considered variables are presented graphically and discussions are made.

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“…Anwar and Sherief (1988) completed the boundary integral equation formulation. Sherief et al (2004Sherief et al ( , 2005 extended the theory of generalized thermoelasticity to include micropolar media and thermoelastic diffusion.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

Sherief

Hussein

2011

Transp Porous Med

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In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic material saturated with a liquid is then considered. The surface of the half-space is assumed to be traction free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. Numerical results for the temperature in the elastic body and fluid, displacement of the elastic body, velocity of the fluid, and stresses for both components are obtained and represented graphically.

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Theory of Generalized Micropolar Thermoelasticity and an Axisymmetric Half-Space Problem

Cited by 78 publications

References 24 publications

Fractional model of thermoelasticity for a half‐space overlaid by a thick layer

Fractional model of thermoelasticity for a half‐space overlaid by a thick layer

Micropolar generalized magneto-thermoelasticity with modified Ohm's and Fourier's laws

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

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