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The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues.

Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates.

This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter.

Constructed purely on theoretical mathematical model by considering different parameters and the functions.

The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations.

In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

In this paper, a solid circular cylinder of finite length occupying the space 0⩽r⩽1, 0⩽z⩽h is considered. The purpose of this paper is to adopt a linear hygrothermal effect to analyze the unsteady state responses in a finite long solid cylinder subjected to axisymmetric hygrothermal loading T=T_R and C=C_R at the surface. The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically.

In the present problem, hygrothermoelastic response of a finite solid circular cylinder has been investigated by integral transform technique consisting of Laplace transform, Hankel transform and Fourier-cosine transform. The problem is investigated subjected to prescribed sources. Numerical algorithm has been developed for numerical computation.

The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically.

The work presented here is mostly hypothetical in nature and totally mathematical.

It may be useful for composite materials, composite laminated plates in hygrothermal environment. Also it is having the applications in hygrothermal field where porous media exposed to heat and moisture. The problem investigated will be beneficial for the researcher working in the field thermoelastic diffusion and hygrothermoelastic materials.

Till date, the other authors did the research work on hygrothermal effect of an infinitely long cylinder without thickness. In this paper, the authors consider finite solid cylinder with finite length and discuss the hygrothermal effect within a small range. Second, the material properties are both homogenous and isotropic and are independent of both temperature and moisture.

The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of dual-phase-lag heat transfer and dual-phase-lag diffusion models. The upper and lower surfaces of the ring are traction free and subjected to an axisymmetric heat supply.

The solution is found by using Laplace and Hankel transform technique and a direct approach without the use of potential functions. The analytical expressions of displacements, stresses and chemical potential, temperature and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of time and diffusion and thermal phase-lags are shown on the various components. Some particular cases of result are also deduced from the present investigation.

It is observed that change in time changes the behaviour of deformations of the various components of stresses, displacements, chemical potential function, temperature change and mass concentration. The authors find that for t=0.2, trends are oscillatory in all the cases whereas for t=0.1, trends are quite different. A sound impact of diffusion and thermal phase-lags on the various quantities is observed. A lot of difference in the trends of single phase lag and dual phase lag is observed. The use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

This problem is totally new because dual phase lag is applied in heat conduction and diffusion equation while considering the problem of plate in axisymmetric heat supply.

This research aims to use the finite element method to examine critical distress modes in the pavement layers due to changes in the structural properties brought upon by fire damage.

A full dynamic analysis is performed to replicate heavy vehicle axle wheel loads travelling over a pavement section.

Results show a 72 per cent decrease in the number of load repetitions which a fire-damaged pavement can experience before fatigue cracking of the asphalt. Further, there is a 51 per cent decrease in loading cycles of the subgrade before rutting of the fire-damaged system.

Fatigue of asphalt and deformation of subgrade from repeated vehicular loading are the most common failure mechanisms, and major attributors to pavement maintenance and rehabilitation costs. Pavement analysis has always been concentrated on evaluating deterioration under regularly occurring operational conditions. However, the impact of one-off events, such as vehicle petroleum fires, has not been evaluated for the effects on deterioration.

The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model.

The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique.

The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter.

Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

The purpose of this paper is to investigate a two dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Three phase lag theory of thermoelasticity has been used to formulate the problem. A numerical inversion technique is applied to obtain the result in the physical domain. The numerical values of the resulting quantities are presented graphically to show the effect of porosity and dual phase lag model. Some particular cases are also presented.

The Laplace and Hankel transforms are employed followed by the eigen value approach to obtain the components of displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain.

This paper fulfils the need to study the two-dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration.

The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration.

The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source.

A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction.

To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered.

This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture.

The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings.

The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models.

To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field.

The purpose of this paper is to study the axisymmetric problem in a micropolar porous thermoelastic circular plate with dual phase lag model by employing eigenvalue approach subjected to thermomechanical sources.

The Laplace and Hankel transforms are employed to obtain the expressions for displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain. A numerical inversion technique has been carried out to obtain the resulting quantities in the physical domain. Effect of porosity and phase lag on the resulting quantities has been presented graphically. The results obtained for Lord Shulman theory (L-S, 1967) and coupled theory of thermoelasticity are presented as the particular cases.

The variation of temperature distribution is similar for micropolar thermoelastic with dual (MTD) phase lag model and coupled theory of thermoelasticity. The variation is also similar for tangential couple stress for MTD and L-S theory but opposite to couple theory. The behavior of volume fraction field and tangential couple stress for L-S theory and coupled theory are observed opposite. The values of all the resulting quantities are close to each other away from the sources. The variation in tangential stress, tangential couple stress and temperature distribution is more uniform.

The results are original and new because the authors presented an eigenvalue approach for two dimensional problem of micropolar porous thermoelastic circular plate with dual phase lag model. A comparison of porosity, L-S theory and coupled theory of micropolar thermoelasticity is made. Such problem has applications in material science, industries and earthquake problems.

A. Conformal Transformation Methods A standard analytic method for the determination of field and potential distributions uses the Schwarz‐Christoffel (SC) conformal transformation integral. When applied to configurations such as the capacitor with fringing accounted for or a metal stripe separated by a dielectric from a ground plane, it leads to complicated expressions containing elliptic integrals, and when applied to a metal disc separated from a ground plane, Hankel transforms are also involved. Since elliptic integrals must be evaluated numerically in practice, it is desirable to replace these complicated analytic processes with one that is numerical from the start. Such a method has been published by Foster, Anderson, and Warner. It is based on the standardization of a two‐step conformal transform; Step 1 takes the original geometry and lays it out along the real axis and Step 2 converts this arrangement—using a reverse Schwarz‐Christoffel transform—into a rectangular structure from which the field lines and equipotentials can be determined by inspection. Step 1 is different for each problem but Step 2 is common to all problems, and represents one of several advantages of this procedure. The simplest example given by the originators is the tri‐plate strip line of Figure 1, which—by symmetry—can be reduced to the quadrant of Figure 2. The SC