Magneto-rotation-fibre-reinforced thermoelastic with gravity and energy dissipation

In this article, two theories of the generalized thermoelasticity Green-Naghdi theory (of type II and III) are applied, as well as the coupled theory to study the effect of magnetic field and rotation under influence of gravity on 2D problem of a fibre-reinforced thermoelastic. The normal mode analysis is used to obtain the expressions for the temperature, displacement components and the thermal stresses distributions. The resulting formulation is applied for two different concrete problems. The first concerns the case of a punch moving across the surface of semi-infinite thermoelastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subjected to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. A comparison is made with the results predicted obtained by the two theories in the presence and absence of magnetic field, rotation and gravity field.     

A three-dimensional thermoelastic problem for a half-space without energy dissipation

A three-dimensional problem for a homogeneous, isotropic and thermoelastic half-space subjected to a time-dependent heat source on the boundary of the space, which is traction free, is considered in the context of Green and Naghdi model II (thermoelasticity without energy dissipation) of thermoelasticity. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the temperature, thermal stress, strain and displacement distributions are represented graphically and discussed.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.     

A two-dimensional generalized thermoelastic diffusion problem for a half-space subjected to harmonically varying heating

A two-dimensional problem for a thermoelastic half-space is considered within the context of the theory of generalized thermoelastic diffusion with one relaxation time. The upper surface of the half-space is taken to be traction free and subjected to harmonically varying heating with constant angular frequency of thermal vibration. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transforms. Numerical results are discussed and represented graphically.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space with Energy Dissipation

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Green and Naghdi theory under the effect of magnetic field is discussed. The problem has been solved analytically using normal mode analysis to obtain the exact solution of the temperature, the displacement components, and the thermal stress. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by types II and III in the presence and in the absence of the effect of a magnetic field and fiber reinforcement. It is found that the reinforcement and magnetic field have great effects on the distribution of the field quantities.     

The Effect of Rotation on Two-Dimensional Problem of a Fiber-Reinforced Thermoelastic with One Relaxation Time

In this article, the Lord–Shulman (L–S) theory with one relaxation time and coupled theory are applied to study the influence of reinforcement on the total deformation of a rotating thermoelastic half-space and the interaction with each other. The problem of a thermal shock has been solved numerically using normal mode analysis. Numerical results for the temperature, displacement, and thermal stress components are given and illustrated graphically for both L–S and coupled theories.     

A Generalized Thermoelasticity Problem for a Half-Space with Heat Sources and Body Forces

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.     

Fractional Order Thermoelasticity Theory for a Half-Space Subjected to an Axisymmetric Heat Distribution

The present work is concerned with a traction-free thermoelastic half-space subjected to a known axisymmetric temperature distribution. The thermoelastic interactions inside the medium are investigated by employing the fractional order theory of thermoelasticity. The problem is solved by using Laplace's and Hankel's transforms. The inverse transforms are computed numerically. The variations of temperature, displacements, and stresses inside the half-space are investigated. The field variables for a particular material are graphically presented. Comparisons are made within the theory in the presence and absence of fractional order parameter.     

A Nonlinear Generalized Thermoelasticity Model of Temperature-Dependent Materials Using Finite Element Method

In this article, a general finite element method (FEM) is proposed to analyze transient phenomena in a thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time. The exact solution of the nonlinear model of the thermal shock problem of a generalized thermoelastic half-space of temperature-dependent materials exists only for very special and simple initial- and boundary problems. In view of calculating general problems, a numerical solution technique is to be used. For this reason, the FEM is chosen. The results for the temperature increment, the stress components, and the displacement component are illustrated graphically with some comparisons.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

A Thick Plate Problem in the Theory of Generalized Thermoelastic Diffusion

In this work, the problem of a thermoelastic thick plate with a permeating substance in contact with one of the bounding planes is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and is subjected to a time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques. The temperature, displacement, stress, and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.     

Wave Propagation in a Magneto-Micropolar Thermoelastic Medium with Two Temperatures for Three-Phase-Lag Model

The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal heat source. The formulation of the problem is applied in the context of the three-phase-lag model and Green-Naghdi theory without dissipation. The medium is a homogeneous isotropic thermoelastic in the half-space. The exact expressions of the considered variables are obtained by using normal mode analysis. Comparisons are made with the results in the two theories in the absence and presence of the magnetic field as well as the two-temperature parameter. A comparison is also made in the two theories for different values of an internal heat source.     

A finite element formulation for thermoelastic damping analysis

We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well‐known Biot's variational principle of thermoelasticity. The coupled finite element equations are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first is a new 8‐node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three‐dimensional 20‐node iso‐parametric thermoelastic element, which is suitable to model massive structures. For the 8‐node element the dissipation along the plate thickness has been taken into account by introducing a through‐the‐thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled‐field elements. Copyright © 2008 John Wiley & Sons, Ltd.     

Deformation due to Mechanical and Thermal Sources in a Thermoelastic Body with Voids under Axi-symmetric Distributions

The Laplace and Hankel transforms have been employed to find the general solution of a homogeneous, isotropic, thermoelastic half-space with voids for a plane axi-symmetric problem. The application of a thermoelastic half-space with voids subjected to a normal force and a thermal source acting at the origin has been considered to show the utility of the solution obtained. To obtain the solution in a physical form, a numerical inversion technique has been applied. The results in the form of displacements, stresses, temperature distribution, and change in volume fraction field are computed numerically and illustrated graphically for a magnesium crystal-like material to depict the effects of voids in the theory of coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for an insulated boundary and a temperature gradient boundary.     

Generalized thermoelastic waves in spherical curved plates without energy dissipation

In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic waves.     

Plane Waves of a Fiber-Reinforcement Magneto-thermoelastic Comparison of Three Different Theories

In this article, the coupled theory, Lord–Shulman theory, and Green–Lindsay (GL) theory are used to study the influence of a magnetic field on a fiber-reinforced thermoelastic half-space. Normal mode analysis is used to solve a thermal shock problem. Numerical results for the temperature, displacement components, and stress components are given and illustrated graphically. A comparison is made between the coupled and GL theories in the absence and presence of a magnetic field and reinforcement.     

Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP) and quasi-SV (qSV) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle     

Effect of mechanical force,rotation and moving internal heat source on a two-temperature fiber-reinforced thermoelastic medium with two theories

In the present paper, the three-phase-lag model and Green–Naghdi theory without energy dissipation are used to study the effect of a mechanical force and a rotation on the wave propagation in a two-temperature fiber-reinforced thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. The methodology applied here is the use of the normal mode analysis to solve the problem of a thermal shock problem to obtain the exact expressions of the displacement components, force stresses, thermal temperature, and conductivity temperature. Numerical results for the considered variables are given and illustrated graphically in the absence and presence of a rotation as well as a mechanical force. A comparison is made with the results in the context of the two theories in the absence and presence of a moving internal heat source.     

Two-dimensional problem for a half-space with axi-symmetric distribution in the theory of generalized thermoelastic diffusion

In this work, we study a two-dimensional problem of axi-symmetric distribution of temperatures in a half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The surface of the half-space is taken as traction free and subjected to axi-symmetric time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. The Laplace and Hankel transform techniques are used. The analytical solution in the transform domain is obtained by using a direct approach. The inverse of the double transform is obtained by using a numerical method based on Fourier expansion techniques. Numerical results for the temperature, displacement, stress, concentration, and chemical potential are carried out and represented graphically.