Nasser El-Maghraby - Academia.edu (original) (raw)

Papers by Nasser El-Maghraby

European Journal of Mechanics - A/Solids, 2006

ABSTRACT In this paper, we will consider a half-space filled with an elastic material, which has ... more 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 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.

Chinese Journal of Physics

Mechanics Based Design of Structures and Machines, 2020

In this work, a 2D axisymmetric problem for an infinite body is considered. An infinite cylinder ... more In this work, a 2D axisymmetric problem for an infinite body is considered. An infinite cylinder composed of a different material and containing a variable heat source lies inside the body. The medium is assumed to be initially quiescent. The theory used is that of thermoelasticity due to Green-Lindsay. The solution is obtained by exponential Fourier and Laplace transform techniques. The inversion process is carried out numerically. Numerical results are computed for the temperature, stress distributions, and displacement and shown graphically.

Mathematical Methods in the Applied Sciences, 2019

We consider a 2D problem for an infinite body with a cylindrical cavity formed of a thermoelastic... more We consider a 2D problem for an infinite body with a cylindrical cavity formed of a thermoelastic substance. The body is under the action of a nonsolenoidal body force. The theory used is that of Generalized Thermoelasticity. The surface is assumed to be traction free and subjected to an asymmetrical thermal shock. Laplace transform is used. The inversion process is carried out numerically. All the relevant functions are represented graphically.

Mathematics and Mechanics of Solids, 2016

A one-dimensional problem for a thermoelastic half-space is considered within the context of the ... more A one-dimensional problem for a thermoelastic half-space is considered within the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface is traction free and subjected to a time dependent thermal shock. Two types of boundary conditions are considered, deterministic and stochastic. A permeating substance is considered in contact with the bounding surface. Laplace transform technique is used to obtain the solution in the transformed domain by using a direct approach. Analysis of wave propagation in the medium is presented. The solution in the physical domain for temperature, displacement, stress, concentration and chemical potential are obtained in an approximate manner. Numerical results are carried out and represented graphically.

Journal of Thermal Stresses, 2009

The two-dimensional problem for a thick plate whose upper surface is subjected to a known tempera... more The two-dimensional problem for a thick plate whose upper surface is subjected to a known temperature distribution, while the lower surface is laid on a rigid foundation and thermally insulated is considered within the context of the theory of thermoelasticity with two relaxation times under the action of a body force. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Journal of Thermal Stresses, 2005

In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside... more In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside the medium. The Fourier and Laplace transform techniques are used. The problem is reduced to the solution of a system of four dual integral equations. The solution of these equations is shown to be equivalent to the solution of a Fredholm integral equation of the first kind. This integral equation is solved numerically using the method of regularization. The inverse Laplace transforms are obtained numerically using a method based on Fourier expansion techniques. Numerical values for the temperature, stress, displacement, and the stress intensity factor are obtained and represented graphically.

Journal of Thermal Stresses, 2004

In this work, a two-dimensional problem for a half-space is solved. The problem is in the context... more In this work, a two-dimensional problem for a half-space is solved. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. The surface of the half-space is taken to be traction free and the temperature on it is specified. Heat sources permeate the medium. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Journal of Thermal Stresses, 2003

An Internal Penny Shaped-Crack in an Infinite Thermoelastic Solid In this work, we solve a dynami... more An Internal Penny Shaped-Crack in an Infinite Thermoelastic Solid In this work, we solve a dynamical problem for an infinite thermoelastic solid with an internal penny-shaped crack, which is subjected to prescribed temperature and stress distributions. The problem is solved using the Laplace and Hankel transforms. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of the second kind, which is solved numerically. The inverse Hankel and Laplace transforms are obtained using a numerical technique. Numerical results for the temperature, stress, and displacement distributions, as well as for the stress intensity factor, are shown graphically.

Journal of Thermal Stresses, 2005

A Two-Dimensional Problem for a Thick Plate with Heat Sources in Generalized Thermoelasticity n t... more A Two-Dimensional Problem for a Thick Plate with Heat Sources in Generalized Thermoelasticity n this work, a two-dimensional problem for a thick plate is solved. The upper surface of the plate is traction free and subjected to a known temperature distribution, while the lower surface is laid on a rigid foundation and thermally insulated. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one and two relaxation times. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

International Journal of Thermophysics, 2009

Computers & Mathematics with Applications, 2013

Effect of body forces on a 2D generalized thermoelastic long cylinder In this work, we consider a... more Effect of body forces on a 2D generalized thermoelastic long cylinder In this work, we consider a two-dimensional problem for an infinitely long solid cylinder. The lateral surface of the cylinder is taken to be traction free and is subjected to a known temperature distribution under the action of solenoidal body forces. Laplace transform techniques are used. The solution in the transformed domain is obtained by using a direct approach in the form of an infinite series. The inverse Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques. Numerical results are computed for the temperature, displacement and stress distributions and shown graphically.

Computational Mathematics and Modeling, 2006

In this work the equations of thermoelasticity with two relaxation times for one-dimensional prob... more In this work the equations of thermoelasticity with two relaxation times for one-dimensional problem are cast into matrix form using the state space and the Laplace transform techniques. The resulting formulation is applied to a half-space problem with thermal shock and vibrational stress. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for temperature, displacement, and stress distributions are given and illustrated graphically. Formulation of the Problem We shall consider a thermoelastic medium governed by the equations of thermoelasticity with two relaxation times whose state depends only on the space variable x and the time variable t. The initial con

Applied Mathematics and Computation, 2005

A Two-Dimensional Thermoelasticity Problem for Thermomechanical Shock with Two Relaxation Times I... more A Two-Dimensional Thermoelasticity Problem for Thermomechanical Shock with Two Relaxation Times In this work a two-dimensional problem of thermoelasticity with two relaxation times is introduced. Laplace and Fourier transform techniques are used. The resulting formulation is applied to a thermomechanical shock half-space problem. The solution in the transformed domain obtained by using a direct approach. Numerical inversion of both transforms is carried out to obtain the temperature, stress and displacement distributions in the physical domain. Numerical results are represented graphically.

Applied Mathematics and Computation, 2004

In this work the state space formulation for one-dimensional problem of generalized thermoelastic... more In this work the state space formulation for one-dimensional problem of generalized thermoelasticity with one relaxation time is introduced. The resulting formulation together with the Laplace transform technique is applied to a thermomechanical shock half-space problem. The solution in the transformed domain is obtained. The inverse Laplace transforms is evaluated numerically. The results are obtained and represented graphically.

Applied Mathematical Modelling, 2013

Stochastic thermal shock problem in generalized thermoelasticity In this work, we consider the pr... more Stochastic thermal shock problem in generalized thermoelasticity In this work, we consider the problem of a half space in the context of the theory of generalized thermoelasticity with one relaxation time. Realistically, the boundary conditions of the problem are considered to be stochastic. Laplace transform technique is used to solve the problem. The boundary conditions are considered to be of a type white noise. The inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time. Numerical results are given and represented graphically.

International Journal of Thermophysics, 2010

In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a ... more In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a linear theory of a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane is considered. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

European Journal of Mechanics - A/Solids, 2006

ABSTRACT In this paper, we will consider a half-space filled with an elastic material, which has ... more 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 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.

Chinese Journal of Physics

Mechanics Based Design of Structures and Machines, 2020

In this work, a 2D axisymmetric problem for an infinite body is considered. An infinite cylinder ... more In this work, a 2D axisymmetric problem for an infinite body is considered. An infinite cylinder composed of a different material and containing a variable heat source lies inside the body. The medium is assumed to be initially quiescent. The theory used is that of thermoelasticity due to Green-Lindsay. The solution is obtained by exponential Fourier and Laplace transform techniques. The inversion process is carried out numerically. Numerical results are computed for the temperature, stress distributions, and displacement and shown graphically.

Mathematical Methods in the Applied Sciences, 2019

We consider a 2D problem for an infinite body with a cylindrical cavity formed of a thermoelastic... more We consider a 2D problem for an infinite body with a cylindrical cavity formed of a thermoelastic substance. The body is under the action of a nonsolenoidal body force. The theory used is that of Generalized Thermoelasticity. The surface is assumed to be traction free and subjected to an asymmetrical thermal shock. Laplace transform is used. The inversion process is carried out numerically. All the relevant functions are represented graphically.

Mathematics and Mechanics of Solids, 2016

A one-dimensional problem for a thermoelastic half-space is considered within the context of the ... more A one-dimensional problem for a thermoelastic half-space is considered within the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface is traction free and subjected to a time dependent thermal shock. Two types of boundary conditions are considered, deterministic and stochastic. A permeating substance is considered in contact with the bounding surface. Laplace transform technique is used to obtain the solution in the transformed domain by using a direct approach. Analysis of wave propagation in the medium is presented. The solution in the physical domain for temperature, displacement, stress, concentration and chemical potential are obtained in an approximate manner. Numerical results are carried out and represented graphically.

Journal of Thermal Stresses, 2009

The two-dimensional problem for a thick plate whose upper surface is subjected to a known tempera... more The two-dimensional problem for a thick plate whose upper surface is subjected to a known temperature distribution, while the lower surface is laid on a rigid foundation and thermally insulated is considered within the context of the theory of thermoelasticity with two relaxation times under the action of a body force. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Journal of Thermal Stresses, 2005

In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside... more In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside the medium. The Fourier and Laplace transform techniques are used. The problem is reduced to the solution of a system of four dual integral equations. The solution of these equations is shown to be equivalent to the solution of a Fredholm integral equation of the first kind. This integral equation is solved numerically using the method of regularization. The inverse Laplace transforms are obtained numerically using a method based on Fourier expansion techniques. Numerical values for the temperature, stress, displacement, and the stress intensity factor are obtained and represented graphically.

Journal of Thermal Stresses, 2004

In this work, a two-dimensional problem for a half-space is solved. The problem is in the context... more In this work, a two-dimensional problem for a half-space is solved. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. The surface of the half-space is taken to be traction free and the temperature on it is specified. Heat sources permeate the medium. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Journal of Thermal Stresses, 2003

An Internal Penny Shaped-Crack in an Infinite Thermoelastic Solid In this work, we solve a dynami... more An Internal Penny Shaped-Crack in an Infinite Thermoelastic Solid In this work, we solve a dynamical problem for an infinite thermoelastic solid with an internal penny-shaped crack, which is subjected to prescribed temperature and stress distributions. The problem is solved using the Laplace and Hankel transforms. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of the second kind, which is solved numerically. The inverse Hankel and Laplace transforms are obtained using a numerical technique. Numerical results for the temperature, stress, and displacement distributions, as well as for the stress intensity factor, are shown graphically.

Journal of Thermal Stresses, 2005

A Two-Dimensional Problem for a Thick Plate with Heat Sources in Generalized Thermoelasticity n t... more A Two-Dimensional Problem for a Thick Plate with Heat Sources in Generalized Thermoelasticity n this work, a two-dimensional problem for a thick plate is solved. The upper surface of the plate is traction free and subjected to a known temperature distribution, while the lower surface is laid on a rigid foundation and thermally insulated. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one and two relaxation times. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

International Journal of Thermophysics, 2009

Computers & Mathematics with Applications, 2013

Effect of body forces on a 2D generalized thermoelastic long cylinder In this work, we consider a... more Effect of body forces on a 2D generalized thermoelastic long cylinder In this work, we consider a two-dimensional problem for an infinitely long solid cylinder. The lateral surface of the cylinder is taken to be traction free and is subjected to a known temperature distribution under the action of solenoidal body forces. Laplace transform techniques are used. The solution in the transformed domain is obtained by using a direct approach in the form of an infinite series. The inverse Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques. Numerical results are computed for the temperature, displacement and stress distributions and shown graphically.

Computational Mathematics and Modeling, 2006

In this work the equations of thermoelasticity with two relaxation times for one-dimensional prob... more In this work the equations of thermoelasticity with two relaxation times for one-dimensional problem are cast into matrix form using the state space and the Laplace transform techniques. The resulting formulation is applied to a half-space problem with thermal shock and vibrational stress. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for temperature, displacement, and stress distributions are given and illustrated graphically. Formulation of the Problem We shall consider a thermoelastic medium governed by the equations of thermoelasticity with two relaxation times whose state depends only on the space variable x and the time variable t. The initial con

Applied Mathematics and Computation, 2005

A Two-Dimensional Thermoelasticity Problem for Thermomechanical Shock with Two Relaxation Times I... more A Two-Dimensional Thermoelasticity Problem for Thermomechanical Shock with Two Relaxation Times In this work a two-dimensional problem of thermoelasticity with two relaxation times is introduced. Laplace and Fourier transform techniques are used. The resulting formulation is applied to a thermomechanical shock half-space problem. The solution in the transformed domain obtained by using a direct approach. Numerical inversion of both transforms is carried out to obtain the temperature, stress and displacement distributions in the physical domain. Numerical results are represented graphically.

Applied Mathematics and Computation, 2004

In this work the state space formulation for one-dimensional problem of generalized thermoelastic... more In this work the state space formulation for one-dimensional problem of generalized thermoelasticity with one relaxation time is introduced. The resulting formulation together with the Laplace transform technique is applied to a thermomechanical shock half-space problem. The solution in the transformed domain is obtained. The inverse Laplace transforms is evaluated numerically. The results are obtained and represented graphically.

Applied Mathematical Modelling, 2013

Stochastic thermal shock problem in generalized thermoelasticity In this work, we consider the pr... more Stochastic thermal shock problem in generalized thermoelasticity In this work, we consider the problem of a half space in the context of the theory of generalized thermoelasticity with one relaxation time. Realistically, the boundary conditions of the problem are considered to be stochastic. Laplace transform technique is used to solve the problem. The boundary conditions are considered to be of a type white noise. The inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time. Numerical results are given and represented graphically.

International Journal of Thermophysics, 2010

In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a ... more In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a linear theory of a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane is considered. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.