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Hamdy M Youssef - One of the best experts on this subject based on the ideXlab platform.
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theory of generalized Thermoelasticity with fractional order strain
Journal of Vibration and Control, 2016Co-Authors: Hamdy M YoussefAbstract:In this work, a new theory of Thermoelasticity has been derived based on fractional order of strain (fraction order Duhamel-Neumann stress-strain relation). A new unified system of differential equations that govern seven different models of Thermoelasticity in the context of one temperature type and two-temperature types (14 different models of Thermoelasticity) has been constructed. The second part of this work, applications of Thermoelasticity with fractional order strain for an isotropic and homogenous one-dimensional elastic half-space based on one-temperature Thermoelasticity of Biot, Lord-Shulman, Green-Lindsay and Green-Naghdi type II models have been solved.
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thermoelastic material response due to laser pulse heating in context of four theorems of Thermoelasticity
Journal of Thermal Stresses, 2014Co-Authors: Hamdy M Youssef, A A ElbaryAbstract:This article describes the study of induced temperature and stress fields in an elastic half-space in the context of classical coupled Thermoelasticity (Biot) and generalized Thermoelasticity (Lord–Shulman, Green–Lindsay and Green–Naghdi) in a unified system of equations. The medium is considered to be made of an isotropic homogeneous thermoelastic half-space. The bounding plane of the surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Because the response is of more interest in the transient state, the inversion of Laplace transforms were carried out numerically. The derived expressions were computed numerically for copper, and the results are presented in graphical form.
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theory of two temperature Thermoelasticity without energy dissipation
Journal of Thermal Stresses, 2011Co-Authors: Hamdy M YoussefAbstract:This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of Thermoelasticity. In particular, in this work, a new theory of generalized Thermoelasticity has been constructed by taking into account two-temperature generalized Thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear Thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized Thermoelasticity without energy dissipation.
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state space approach of two temperature generalized Thermoelasticity of one dimensional problem
International Journal of Solids and Structures, 2007Co-Authors: Hamdy M Youssef, Eman A N AllehaibiAbstract:Abstract In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized Thermoelasticity theory [Youssef, H., 2005a. The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized Thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26(4), 4827; Youssef, H., 2005b. Theory of two-temperature generalized Thermoelasticity, IMA J. Appl. Math., 1–8]. The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and traction free. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature parameter.
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two dimensional generalized Thermoelasticity problem for a half space subjected to ramp type heating
European Journal of Mechanics A-solids, 2006Co-Authors: Hamdy M YoussefAbstract:In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in a unified system from which the field equations for coupled Thermoelasticity as well as for generalized Thermoelasticity can be easily obtained as particular cases. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating. The inverse Fourier transforms are obtained analytically while the inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating with different theories of Thermoelasticity.
Ashraf M Zenkour - One of the best experts on this subject based on the ideXlab platform.
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magneto thermal shock for a fiber reinforced anisotropic half space studied with a refined multi dual phase lag model
Journal of Physics and Chemistry of Solids, 2020Co-Authors: Ashraf M ZenkourAbstract:Abstract A novel model of multi-dual-phase-lag generalized magneto-Thermoelasticity is presented. It is applied to treat a thermal shock for a fiber-reinforced anisotropic half-space. The medium is subjected to a primary magnetic field as well as a thermal shock. The normal mode technique is applied to solve the coupled differential equations and the physical fields are derived. Different mechanical and thermal loads are applied on the surface of the medium. Validation examples are presented and results due to different theories are compared. The effects of the magnetic field parameter and different Thermoelasticity theories on all physical fields are investigated.
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multi thermal relaxations for thermodiffusion problem in a thermoelastic half space
International Journal of Heat and Mass Transfer, 2019Co-Authors: Ashraf M Zenkour, Marwan Amin KutbiAbstract:Abstract This paper presents a novel multi-phase-lag model to study the thermoelastic diffusion behaviour of a one-dimensional half-space. The multi-phase-lag, the Green–Lindsay, the Lord–Shulman models as well as the classical theory of Thermoelasticity are mutual into a unified formulation. The exact solution of three coupled equations, namely; motion, heat conduction and mass diffusion equations; has been obtained. Solutions determining for initial and boundary conditions are considered to define the thermoelastic diffusion behavior of the medium. The validity of results is acceptable by comparing the temperature, dilatation, displacement, stresses, concentration, and chemical potential according to the present multi-phase-lag theory with those due to other Thermoelasticity theories.
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three dimensional thermal shock plate problem within the framework of different Thermoelasticity theories
Composite Structures, 2015Co-Authors: Ashraf M ZenkourAbstract:Abstract The exact three-dimensional solutions of the temperature, displacements and stresses of thermal shock plate problem are presented. The bottom surface of the plate is thermally isolated while the upper one is subjected to a thermal shock. A unified generalized Thermoelasticity theory for the transient thermal shock plate problem in the context of Green and Lindsay, Lord and Shulman, and coupled Thermoelasticity theories is presented. The variations along the longitudinal and thickness directions of all fields are investigated. Some comparisons have been shown graphically to estimate the effects of different parameters on all the studied fields. The analytical general solution is applied to the present plate using the normal mode analysis. A comparison between different theories is presented and suitable conclusions are made.
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state space approach for an infinite medium with a spherical cavity based upon two temperature generalized Thermoelasticity theory and fractional heat conduction
Zeitschrift für Angewandte Mathematik und Physik, 2014Co-Authors: Ashraf M Zenkour, Ahmed E AbouelregalAbstract:This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity. A general solution to the problem based on the two-temperature generalized Thermoelasticity theory (2TT) is introduced. The theory of thermal stresses based on the heat conduction equation with Caputo’s time-fractional derivative of order α is used. Some special cases of coupled Thermoelasticity and generalized Thermoelasticity with one relaxation time are obtained. The general solution is provided by using Laplace’s transform and state-space techniques. It is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading (thermal shock). Some numerical analyses are carried out using Fourier’s series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically and the effects of two-temperature and fractional-order parameters are discussed.
B Straughan - One of the best experts on this subject based on the ideXlab platform.
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a note on discontinuity waves in type iii Thermoelasticity
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2004Co-Authors: Ramon Quintanilla, B StraughanAbstract:Two recent nonlinear theories of Thermoelasticity, developed by Green and Naghdi, are examined. It is shown that in type II theory, second sound is permissible and both mechanical and temperature waves may propagate. In type III theory we show that the situation is more analogous to that in classical nonlinear Thermoelasticity: one wave propagates and a homothermal temperature wave is allowed.
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growth and uniqueness in Thermoelasticity
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2000Co-Authors: Ramon Quintanilla, B StraughanAbstract:A uniqueness theorem is proved for two theories of Thermoelasticity capable of admitting finite speed thermal waves, the theories having been proposed by Green & Naghdi. Uniqueness is proved under ...
Ahmed E Abouelregal - One of the best experts on this subject based on the ideXlab platform.
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fibre reinforced generalized anisotropic thick plate with initial stress under the influence of fractional Thermoelasticity theory
Advances in Applied Mathematics and Mechanics, 2017Co-Authors: Ahmed E AbouelregalAbstract:In the present work concentrated on the two-dimensional problem of generalized Thermoelasticity for a fiber-reinforced anisotropic thick plate under initial stress. Using generalized Thermoelasticity theory with fractional order heat conduction, the problem has been solved by a normal mode analysis. The effect of hydrostatic initial stresses and fractional order parameter is shown graphically on the distributions of the temperature, displacement and thermal stress components. It is found from the graphs that the initial stress and the fractional parameter significantly influences the varieties of field amounts.
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state space approach for an infinite medium with a spherical cavity based upon two temperature generalized Thermoelasticity theory and fractional heat conduction
Zeitschrift für Angewandte Mathematik und Physik, 2014Co-Authors: Ashraf M Zenkour, Ahmed E AbouelregalAbstract:This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity. A general solution to the problem based on the two-temperature generalized Thermoelasticity theory (2TT) is introduced. The theory of thermal stresses based on the heat conduction equation with Caputo’s time-fractional derivative of order α is used. Some special cases of coupled Thermoelasticity and generalized Thermoelasticity with one relaxation time are obtained. The general solution is provided by using Laplace’s transform and state-space techniques. It is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading (thermal shock). Some numerical analyses are carried out using Fourier’s series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically and the effects of two-temperature and fractional-order parameters are discussed.
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generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat
Meccanica, 2013Co-Authors: Ahmed E AbouelregalAbstract:In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized Thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled Thermoelasticity, generalized Thermoelasticity with one relaxation time, and Thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.
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electromagneto thermoelastic problem in a thick plate using green and naghdi theory
International Journal of Engineering Science, 2009Co-Authors: M N M Allam, Khaled A Elsibai, Ahmed E AbouelregalAbstract:The two-dimensional problem of electromagneto-Thermoelasticity for a homogeneous isotropic perfectly conducting thick plate subjected to a time-dependent heat source is studied in the context of Green and Naghdi theory of Thermoelasticity. The normal mode analysis is used to obtain the exact expressions for temperature distribution, thermal stresses, and displacement components. The results are shown graphically to study the effect of Green and Naghdi parameter and the influence of electromagnetic waves.
Magdy A Ezzat - One of the best experts on this subject based on the ideXlab platform.
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on phase lag green naghdi theory without energy dissipation for electro Thermoelasticity including heat sources
Mechanics Based Design of Structures and Machines, 2019Co-Authors: Sayed I Elattar, Mohamed H Hendy, Magdy A EzzatAbstract:A mathematical model of electro-Thermoelasticity has been constructed in the context of a new consideration of heat conduction with phase-lag Green-Naghdi theory without energy dissipation (GN-II)....
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unified gn model of electro Thermoelasticity theories with fractional order of heat transfer
Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems, 2018Co-Authors: Magdy A Ezzat, A A ElbaryAbstract:A unified mathematical model of electro-Thermoelasticity has been constructed in the context of a new consideration of heat conduction law with fractional order derivative. Some essential theories follow as limit cases. The governing coupled equations are applied to several concrete problems: (a) time-dependent thermal shock problem; (b) a problem for a half-space subjected to an arbitrary heating and (c) a layer media problem. Laplace transforms are used to derive the solution in the Laplace transform domain. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory, Lord–Shulman, Green–Naghdi (GN) and fractional coupled Thermoelasticity theories. The result provides a motivation to investigate conducting fractional thermoelectric materials as a new class of applicable materials.
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two temperature theory in green naghdi Thermoelasticity with fractional phase lag heat transfer
Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems, 2018Co-Authors: Magdy A Ezzat, Ahmed S Elkaramany, A A ElbaryAbstract:A mathematical model of two-temperature phase-lag Green–Naghdi thermoelasticty theories based on fractional derivative heat transfer is given. The GN theories as well as the theories of coupled and of generalized Thermoelasticity with thermal relaxation follow as limit cases. The resulting non dimensional coupled equations together with the Laplace transforms techniques are applied to a specific problem of a half space subjected to arbitrary heating which is taken as a function of time and is traction free. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of Thermoelasticity with one relaxation time. The effects of temperature discrepancy and fractional order parameters on copper-like material are discussed in different types of GN theories.
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modeling of memory dependent derivative in generalized Thermoelasticity
European Physical Journal Plus, 2016Co-Authors: Magdy A Ezzat, Ahmed S Elkaramany, A A ElbaryAbstract:The generalized thermoelasticty equations based on memory-dependent derivative (MDD) is modeled so that some essential theories can be easily obtained. The exact solutions for different problems in Laplace transform domain are obtained. A numerical method is employed for the inversion of the Laplace transforms. The results are compared to those of the indicated theories of generalized Thermoelasticity. The effects of the time-delay on Thermoelasticity for different linear forms of Kernel functions are discussed.
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generalized Thermoelasticity with memory dependent derivatives involving two temperatures
Mechanics of Advanced Materials and Structures, 2016Co-Authors: Magdy A Ezzat, Ahmed S Elkaramany, A A ElbaryAbstract:ABSTRACTA new generalized model of two-temperature Thermoelasticity theory with time-delay and Kernel function is constructed. Taylor theorem in terms of memory-dependent derivatives is proved. The governing coupled equations of the new generalized Thermoelasticity with time-delay and Kernel function, which can be chosen freely according to the necessity of applications, are applied to a one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. Laplace transforms technique will be used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory have been constructed. Some comparisons are shown in the figures to estimate the effects of the temperature discrepancy and time-delay parameter on all of the studied fields.
