Ahmed Fouad Ghaleb

• Doctor of Philosophy
• Professor Emeritus at Cairo University

A nonlinear phenomenological model of flexoelectricity in thermoelastic solids is presented within the frame of continuum mechanics and extended thermodynamics, incorporating the quasi-electrostatic approximation where the time derivative of the electric displacement vector can be neglected in Maxwell–Ampère’s law. An expression for the energy flux...

تهدف هذه الدراسة إلى إلقاء الضوء على الحياة العلمية في المملكة المصرية في الربع الثاني من القرن العشرين، استناداً لتلخيص هام كتبه عالمان كبيران زارا كلية العلوم بجامعة فؤاد الأول ربيع 1945، وهما الفيزيائي ماكس بورن وعالم النباتات ليونيل بريمبل. وقد لخص الباحثان الكثير من الأنشطة الأكاديمية في مصر في ذلك الوقت، مؤرخين للإنشاءات الجامعية، والبحوث الع...

The objective is to study the combined effect of an incident wave, a surface pressure excess and a finite number of submerged obstacles, in the phenomenon of power transfer to an infinite fluid layer of finite depth. The incident wave and the surface pressure excess have the same harmonic time dependence, a fact that allows to eliminate time altoge...

The annular Couette flow has several industrial applications, particularly for the characterization of the fluid flow and deformation behavior of fluids. The inclusion of the dynamic wall slip into the flow boundary conditions seems to be necessary for an efficient continuum description of motion of nanofluidics as it reflects the importance of flu...

This work investigates the Flamant-Boussinesq problem for a half-space made of a homogeneous and isotropic dielectric material. The dynamical flexoelectric effect and the dynamical flexocoupling between displacement and polarization, due to mechanical and electrical states, are taken in consideration. The mechanical loading is taken as a wave of a...

We establish convergence analysis for Hermite-type interpolations for L2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2} ( \mathbb {R})$$\end{document}-entire f...

This paper investigates the thermal, variable viscosity axial Couette flow between two con-centric circular cylinders, taking into account both the Navier and the dynamical slip boundary conditions. The nonlinear governing equations for momentum and energy balance are solved under start-up condition using the Laplace transform (LT) technique, in co...

We investigate a one-dimensional restriction of a nonlinear model of thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic regime (see Ghaleb et al. in Int J Eng Sci 119:29–39, 2017. https://doi.org/10.1016/j.ijengsci.2017.06.010). An additional dependence of the thermal conductivity and the thermal relaxation time on t...

We investigate nonlinear Rayleigh wave propagation in a layered thermoelastic medium composed of a slab rigidly bonded to the surface of a half-space under prescribed external thermal boundary conditions within the dual-phase-lag theory. The heat conduction coefficient for both the slab and the matrix have a linear dependence on temperature. Our ai...

The Shannon-Taylor interpolation technique was introduced by Butzer and Engels in 1983. In this work, the sinc-function is replaced by a Taylor approximation polynomial. In this work, we implement the Shannon-Taylor approximations to solve a one-dimensional heat conduction problem. One of the major advantages of this approach is that the resulting...

We investigate nonlinear Rayleigh wave propagation in a layered thermoelastic medium composed of a slab rigidly bonded to the surface of a half-space under prescribed external thermal boundary conditions within the dual-phase-lag theory. The heat conduction coecient for both the slab and the matrix have a linear dependence on temperature. Our aim i...

A model of generalized thermoelasticity within dual-phase-lag is used to investigate nonlinear Rayleigh wave propagation in a half-space of a transversely isotropic elastic material. It is assumed that the coefficient of heat conduction is temperature-dependent, a fact that plays an important role in the coupling behaviour analysis of thermoelastic...

A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flu...

A novel technique is proposed for nding an approximate solution of the strongly nonlinear ordinary dierential equation for the charged damped pendulum with one degree of freedom. The method relies on a transformation of the governing nonlinear dierential equation that keeps unchanged the order of the highest derivative, in conjunction with a modied...

A new semi-analytical approach relying on Legendre finite expansions of the free surface elevation and boundary collocation is proposed to solve the fully nonlinear two-dimensional, steady free-surface wave-free gravity flow in an infinite channel with topography. The fluid is inviscid with constant density and the flow is irrotational. The unknown...

Sampling reconstruction of signals band-limited in the linear canonical transform domain has become a major task in bridging the relationship between the continuous physical signals and discrete signals. Many recent works dealt with this task from different theoretical and practical aspects. Furthermore, and as in the case of the classical Shannon’...

A one-dimensional problem of wave propagation in phononic materials is solved under the reduced micromorphic model introduced recently. An efficient technique is used for the solution, based on one-sided Fourier transform. This allows obtaining an exact solution in closed form, which can be utilized to check approximate solutions obtained by other...

A simple semi-analytical approach relying on Fourier-type finite expansions and boundary collocation is proposed to solve an inverse problem for the fully nonlinear two-dimensional, steady, free-surface, wave-free gravity fluid flow in an infinite channel with topography of finite extent. The fluid is of constant density, and the flow is assumed ir...

We investigate linear, thermoelastic wave propagation in a layered piezoelectric material composed of a slab bonded to a half-space substrate of a dissimilar material, within dual-phase-lag model and under thermomechanical loads. One of the aims of the present work is to formulate a set of boundary conditions that is compatible with the field equat...

This work aims at presenting a new numerical solution to a nonlinear, one-dimensional problem of heat wave propagation in a thick slab of a rigid thermal conductor. The model predicts dependence of second sound velocity on temperature and heat flux. For this, an unconditionally stable numerical scheme is constructed using a kind of weighted average...

We present a numerical solution by finite differences to a linear, plane, initial-boundary-value problem of thermo-piezoelasticity in a quarter-space, within the dual-phase-lag model. Motion is excited by a one-period heat regime applied to one boundary of the medium. The relation between the two relaxation times is clarified in order to obtain wav...

In the light of the potential applications in engineering, electronics, physics, chemistry, and biology, the current work applies several techniques to achieve analytic approximate and numerical solutions of the cubic-quintic Duffing-Van der Pol equation. This equation represents a second-order ordinary differential equation with quintic nonlineari...

The current work is concerned with the study of wave propagation in a half-space of a piezo-thermoelastic material under a bias tangential magnetic field within dual-phase-lag (DPL). This is relevant to the design and performance of piezoelectric devices working under a bias magnetic field, for example, the DC magnetic field piezoelectric sensors w...

Harmonic Cartesian polynomial and rational functions are shown to provide a simple way of obtaining a semi-analytical solution to the uncoupled, two-dimensional problem of thermomagnetoelasticity for a long, transversely isotropic, elastic cylinder carrying an axial, steady electric current. The proposed method involves the solution of a difficult...

We present new nonlinear, one-dimensional equations of extended thermodynamics for temperature and heat flux that describe damped heat wave propagation and predict dependence of the second sound velocity on temperature and heat flux in a rigid thermal conductor. The aim of the present work is to investigate the implications of the considered nonlin...

We investigate the effect of rotation on plane wave propagation in a half-space of a piezo-thermoelastic material within the frame of dual-phase-lag model. Normal mode technique is used to obtain analytic expressions for the displacement components, temperature and stress components. Numerical results for the quantities of practical interest are gi...

A system of N coupled linear boundary Fredholm integral equations of the second kind is derived to describe the electric current system and the magnetic field distribution in space for an infinite plane electrical conducting sheet with N non-overlapping insertions, permeated by a uniform parallel electric field. The cases of one or two insertions o...

This article is concerned with a strain gradient theory for thermoelastic diffusion materials. The work is motivated by the recent interest in the study of gradient theories and increasing use of materials which possess thermal and mass diffusion variations. First, we establish the basic equations of the nonlinear strain gradient theory for thermoe...

The subject of thermo-electroelasticity involves many complications due to the multiple ways in which the mechanical, thermal and electric fields can interact, some of these involving non-linearities. In extended thermodynamics, an additional difficulty arises due to the requirement of finiteness of the speed of propagation of the thermal disturban...

We investigate a nonlinear, one-dimensional problem of thermoelectroelasticity with thermal relaxation and in quasi-electrostatics. The system of basic equations is a restriction to one spatial dimension of that proposed earlier in Abou-Dina et al (2017). This model is based on the introduction of the heat flow vector as an additional state variabl...

A model of nonlinear thermo-electroelasticity is presented within the frame of extended thermodynamics and in the quasi-electrostatic regime. The model is based on a Cattaneo-type evolution equation and includes several couplings between the mechanical, thermal and electric fields, and may therefore be used to describe a broad range of interactions...

A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally...

Using a well-known solution for steady temperature distribution in a rectangle, a boundary integral method is used to obtain an approximate solution for a plane problem of uncoupled thermoelasticity with mixed mechanical boundary conditions. The unknown functions in the cross-section are obtained in the form of series in Cartesian harmonics, enrich...

We find the deformation and stresses in an infinite rod of an electric conducting material with square normal cross section, carrying uniform electric current and subjected to an external, initially uniform magnetic field. The complete solution of the uncoupled problem is obtained using a boundary integral method. The results are discussed in detai...

Generalizing a previous result by two of the authors (MSA and AAA) for an infinite sheet with one insertion, we derive two coupled linear Fredholm integral equations of the second kind on two coplanar contours for the determination of the magnetic field due to an infinite plane electrical conducting sheet with two non-overlapping insertions, permea...

A numerical solution is presented for a nonlinear, one-dimensional boundary-value problem of thermoelasticity with variable volume force and heat supply in a half-space. The surface of the body is subjected to a given periodic displacement. The volume force and bulk heating simulate the effect of a beam of particles infiltrating the medium. No phas...

The static, plane uncoupled problem of thermo-magnetoelasticity for a long elastic cylinder of square cross-section carrying a steady, axial electric current is investigated numerically by a boundary integral method. The lateral surface of the cylinder may be subjected, additionally, to an external distribution of pressures. The deformation is indu...

A numerical boundary integral scheme is proposed for the solution of the system of field equations of plane, linear elasticity in stresses for homogeneous, isotropic media in the domain bounded by an ellipse under mixed boundary conditions. The stresses are prescribed on one half of the ellipse, while the displacements are given on the other half....

The objective is to introduce a semi-analytical method for solving axisymmetric problems of electromagnetic induction in thin spherical caps placed in a time-varying magnetic field due to an axial magnetic dipole or in a time-varying uniform axial magnetic field. This method provides approximate solutions to mathematically difficult mixed boundary-...

A boundary integral method earlier proposed by two of the authors [M. S. Abou-Dina and A. F. Ghaleb, Int. J. Appl. Electromagnet. Mech. 11, 185–201 (2000)] is used to solve a problem of uncoupled magnetothermoelasticity for an infinite elliptical cylindrical conductor carrying a steady axial uniform electric current. The cylinder is placed in a var...

The main objective of the present work is to introduce a variant of Trefftz's method for finding approximate solutions to regular or singular two-dimensional boundary-value problems for Laplace's equation.After expressing the solution as a finite linear combination of trial functions, the method foresees the enforcement of the boundary condition by...

A numerical scheme is proposed for the solution of the system of field equations and boundary conditions of the static, linear plane strain problem of the Theory of Elasticity in stresses. The work is based on a previous analytical approach by the authors within the Boundary Integral Method for a homogeneous and isotropic elastic material occupying...

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore,...

A boundary integral method is used to solve the problem of plane, uncoupled linear thermoelasticity with heat sources for an infinite cylinder with elliptical cross section, subjected to a uniform pressure and to a thermal radiation condition on its boundary. The complete solution of the problem is obtained. The results reduce to those for the infi...

This article investigates the computational aspects of a boundary integral method, previously introduced by two of the authors [11. M. S. Abou-Dina and A. F. Ghaleb , On the Boundary Integral Formulation of the Plane Theory of Thermoelasticity (Analytical Aspects) , J. Thermal Stresses , vol. 25 , pp. 1 – 29 , 2002 . [Taylor & Francis Online], [W...

We investigate the deformation of an infinitely long, circular cylindrical electric conductor carrying a uniform axial current, for the case when the electric conductivity of the coating is temperature dependent. This model conforms with the real situation for many of the existing modern dc cables with polyethylene coating. The distributions of tem...

The purpose of this work is to present a general formulation of the static, linear plane strain problem of uncoupled thermo-magnetoelasticity for isotropic media occupying simply connected regions, based on the combined use of the stress function and of the boundary integral representation technique in terms of real functions. A new representation...

A numerical solution for a one-dimensional, nonlinear wave propagation problem of thermo-magneto-elasticity for the elastic, perfectly conducting half-space is presented. The results are discussed and compared to the case of no magnetic field, to investigate the effect of the latter on the mechanical displacement and on the temperature. The used nu...

A formulation of the plane strain problem of the theory of elasticity in stresses, for simply connected domains, is carried out in terms of real functions within the frame of what is known as the boundary integral method. Special attention is devoted to the problem of determination of the arbitrary constants appearing in the solution, in view of wo...

A numerical solution for a nonlinear, one-dimensional boundary-value problem of thermoelasticity for the elastic half-space is presented. The resulting equations are discussed and the numerical method is investigated for stability. Comparison with other existing numerical schemes is carried out. The obtained results clearly indicate the process of...

Relying on a nonlinear continuum model of thermo-magnetoelasticity previously introduced by the authors, in which the heat capacity of the medium depends on strain and magnetic field, we investigate the effect of this dependence on the one-dimensional propagation of nonlinear, thermo-magnetoacoustic waves in an anisotropic (but centrosymmetric) hal...

A complete set of field equations, constitutive relations and boundary conditions is derived in material form, within the framework of rigorous thermodynamics, to study the nonlinear thermo‐magnetoelastic interactions in anisotropic continuous media for which the specific heat capacity depends on strain and magnetic field. The proposed model includ...

Stresses and displacements are obtained for an elastic superconductor in the form of an infinitely long, circular cylindrical tube subjected to an initially uniform magnetic field perpendicular to the tube's axis. The effect of the magnetic field penetration on the stressed state is assessed by solving the problem, firstly taking into account this...

In this paper, an attempt has been made to study one-dimensional (1-D) wave propagation in a magnetoelastic medium of finite electric conductivity subjected to an initial magnetic field-first longitudinal and then transverse to the direction of propagation—within the frame of a model including the first level of nonlinearity. The second order asymp...

We use the basic equations given in a previous paper [1] to investigate the nonlinear surface wave propagation in an isotropic magnetoelastic half-space having finite electric conductivity and subjected to an initial constant magnetic field normal to the sagital plane. The unknowns of the problem are represented as expansions in a small parameter....

We use the basic equations given in a previous paper by Hefniet al. [1] to investigate the nonlinear surface wave propagation (SWP) in an isotropic magnetothermoelastic (MTE) half-space of perfect electric conductivity subjected to an initial constant magnetic field normal to the sagittal plane. The first and second order approximations are derived...

The penetration of the magnetic field into a superconductor must be taken into account when investigating the stressed state of the body. This is elucidated for the simple example of an infinitely long superconducting cylindrical tube placed in a uniform magnetic field parallel to its axis. It is shown that the stress component σθθ, which is not ex...

The basic equations that describe nonlinear thermoelastic interactions in a continuous medium were derived under the simplifying monomode hypothesis to provide an effective basis for the investigation of nonlinear thermoelastic bulk wave propagation. The one-dimensional equations are solved for a semi-bounded region (half-space) subjected to a pres...

The formulation and solution of a two-dimensional magnetothermoelastostatic boundary value problem is presented for an infinitely long, elliptic cylindrical conductor carrying a steady, uniformly distributed electric current. A linear dependence of the magnetic permeability tensor on strain is taken into account. The analysis involves the solution...

In this paper, we build a phenomenological model for elastic superconductors which relies on rigorous thermodynamics. The basic postulate is the dependence of the free energy of the medium on the electric current density vector and on an objective time derivative of the magnetic field. The entropy flux retains its usual, simple form. A wave type eq...

The aim of this paper is to build a phenomenological model for elastic superconductors that relies on rigorous thermodynamics. This model includes the main two features of superconductors: The zero electrical resistance and Meissner effect. A section is devoted to the so-called magnetic superconductors, in which superconductivity and ferromagnetism...

A one-dimensional, linear heat conduction equation involving three relaxation times is derived for a rigid thermal conductor. Form preserving and plane wave solutions are investigated. Attention is focused on the influence on wave propagation of a dissipation term involving the time derivative of temperature in the expression for entropy. Some nume...

The one-dimensional propagation of weak discontinuities in a rigid thermal conductor is investigated within the frame of extended thermodynamics on the basis of a model proposed earlier by the author [Int. J. Eng. Sci. 24, 765-771 (1986; Zbl 0581.73009)]. It is shown that the presence of a linear term involving the temperature time derivative in th...

The present work is devoted to the study of deformations occurring in an infinitely long, hollow circular cylindrical conductor coated with a coaxial, thick viscoelastic material under the influence of a steady current, within the framework of linear elasticity. The proposed model for both conductor and insulator allows for couplings of the magneto...

In this work we present a thermodynamical phenomenological formulation of a theory capable of displaying electromechanical hysteresis effects in continous media, which should apply to ferroelectric ceramics. This is built within the scheme of the thermodynamical theory of internal variables. This theory produces both plastic and electric-hysteresis...

In this work, we use the model developed in Part I [1] to deduce a consistent set of thermodynamical relations for the description of the poling of ceramics. With the appropriate identifications, these relations can be considered as a thermodynamical basis for Chen's theory which did not rely on thermodynamics. Time-dependent effects (akin to visco...

A double-series asymptotic expansion is used to investigate the steady, two-dimensional, wave-free gravity flow of an incompressible fluid over a bump. New solutions without hydraulic jumps are constructed for both the super- and subcritical regimes. For the latter, the theoretical predictions are in good agreement with experiment in those regions...

The introduction of the heat flow vector and its spatial gradients as arguments in the Helmholtz free energy allows us to derive a new set of constitutive and kinetic equations describing thermoelastic interactions in continuous media. This set includes a generalized Fourier law for heat conduction that accounts for a finite velocity of propagation...

The generalization of Ilyushin's approximation method is used to determine the stresses in the quasistatic problem of torsion of a composite, layered viscoelastic prismatic bar of rectangular cross-section. Numerical computations are carried out for the special case of a step function torsional moment.