Fundamental solution and uniqueness theorems in the linear theory of thermoviscoelasticity for solids with double porosity

In this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with double porosity is considered. The fundamental solution of the system of equations of steady vibrations is constructed by elementary functions and its basic properties are established. The Green’s first identity in the considered theory is obtained. A wide class of the internal and external boundary value problems (BVPs) of steady vibrations is formulated. Finally, on the basis of the Green’s identity, the uniqueness theorems for regular (classical) solutions of these BVPs are proved.     

Potential Method in the Theory of Thermoviscoelasticity for Materials with Voids

In the present article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The Sommerfeld-Kupradze type radiation conditions are established. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The Green's formulas and integral representations of Somigliana type of regular vector and classical solution are obtained. The basic properties of thermoelastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (boundary integral method) and the theory of singular integral equations.     

On the linear theory of double porosity thermoelasticity under local thermal non-equilibrium

In the present paper, the linear theory of thermoelasticity of double porosity materials under local thermal non-equilibrium is considered and the basic boundary value problems are investigated by using the boundary integral equation method (potential method). Indeed, the fundamental solution of system of steady vibrations equations of the considered theory is constructed explicitly by means of elementary functions and its basic properties are established. A Galerkin-type solution to this system of equations is presented and the completeness of this solution is proved. The basic internal and external boundary value problems of steady vibrations are formulated and the uniqueness theorems for classical solutions of these problems are proved. The basic properties of the surface and volume potentials and singular integral operators are established. Finally, the existence theorems for classical solutions of the above-mentioned boundary value problems are proved by using the potential method and the theory of singular integral equations.     

Potential Method in the Linear Theory of Thermoelasticity with Microtemperatures

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. The basic boundary value problems of steady vibrations are investigated using the potential method. Sommerfeld–Kupradze type radiation conditions and the basic properties of thermoelastopotentials are established. The uniqueness and existence theorems of classical solutions of the external (with respect to an unbounded domain) boundary value problems are proved.     

Fundamental Solutions in the Theory of Thermoelasticity for Solids with Double Porosity

In this article, the linear theory of thermoelasticity for solids with double porosity is considered. The fundamental solutions for the systems of steady vibrations (including quasi-static case) and equilibrium equations are constructed by means of elementary functions; the basic properties of such solutions are also established.     

POTENTIAL METHOD IN THE LINEAR THEORY OF BINARY MIXTURES OF THERMOELASTIC SOLIDS

This article deals with the diffusion model of the linear theory of binary mixtures of the thermoelastic solids. A wide class of external (with respect to an unbounded domain) boundary value problems of steady oscillations is investigated using the potential method. Sommerfeld-Kupradze-type radiation conditions are established. The uniqueness and existence theorems of classical solutions of the aforementioned problems are proved.     

FUNDAMENTAL SOLUTIONS IN THE THEORY OF MICROMORPHIC ELASTIC SOLIDS WITH MICROTEMPERATURES

By means of elementary functions, the fundamental solutions of equations of equilibrium and steady oscillations of the theory of micromorphic elastic solids with microtemperatures are constructed, and basic properties are established.     

FUNDAMENTAL SOLUTIONS OF THE EQUATIONS OF THE THEORY OF THERMOELASTICITY WITH MICROTEMPERATURES

By means of elementary functions, the fundamental solutions of the equations of the equlibrium and steady oscillations of the theory of thermoelasticity with microtemperatures are constructed, and basic properties are established.     

Thermal Stresses in Anisotropic and Radially Inhomogeneous Annular Domains

This paper presents an analytical approach for construction of solutions to the plane quasi-static, non-axially-symmetric elasticity and thermoelasticity problems for cylindrically anisotropic and radially inhomogeneous hollow cylinders and disks subjected to in-plane external force loadings and temperature distribution. This approach is based upon the direct integration of equilibrium equations, which are independent of material properties. The original problems are reduced to integral equations of Volterra type. By application of the resolvent technique, solutions of the governing integral equations are constructed in explicit form, which is convenient for analysis and appropriate for various kinds of inhomogeneity.     

边界点法在传热问题数值分析中的应用

将一种新的数值分析方法-边界点法应用于传热问题的研究，对无内热源稳态热传导问题，通过传统边界元法将边界积分方程离散化，发现可以不直接求解影响系数矩阵，而是通过对偶关系，由域外虚源构造方程组的特解场形成边界已知和未知温度，热流密度的系数矩阵，而且域内温度和热流密度的求解将不依赖于边界未知参数的求解，对于有内热源的问题，可以将非齐次方程的解转换为齐次方程的解和某一确定解的叠加，对于非线性问题，可以通过基尔霍夫变换，将非线性问题转化为线性问题求解，这种边界点方法不但具有边界元法降维的优势，而且不须求解奇异积分，大大节约了计算时间，计算精度极高，以有内热源非线性稳态热传导问题的实例印证了这种方法的高效性。     

Transient Thermoelectroelastic Response of a Functionally Graded Piezoelectric Strip with Two Parallel Axisymmetric Cracks

In this article, the problem of two parallel axisymmetric cracks in a plate of a functionally graded piezoelectric material (FGPM) strip is analyzed under transient thermal loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are supposed to be insulated thermally and electrically. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. Systematic numerical calculations are carried out, and the field intensity factors versus time are presented for various values of dimensionless parameters representing the crack geometry and the material non-homogeneity.     

Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium

In this paper, melting effect on mixed convective heat transfer from a porous vertical plate with uniform wall temperature in the liquid-saturated porous medium with aiding and opposing external flows is numerically examined at steady state. The resulting boundary value problems (BVPs) are comprehensively solved by Runge–Kutta–Gill method and Newton’s iteration for similarity solutions. As shown in the results, for aiding and opposing external flows, it is all found that the rate of convective heat transfer at the interface of solid and liquid phases is reduced with increasing melting strength. Additionally, the melting phenomenon decreases the thermal boundary layer regions of mixed convection in a porous medium. With melting effect, the heat transfer rate is also shown to be asymptotically approaching the forced or free convection as the value of Gr/Re approaches the limits of zero and infinity for aiding external flow; and the criteria for pure forced and mixed convection from an isothermal vertical flat plate in porous media with aiding and opposing external flows are established in melting process.     

On the Fundamental Solutions of Generalized Thermoelasticity with Three Phase-Lags

The aim of the present work is to derive the fundamental solutions in the linear theory of generalized thermoelasticity with three phase-lags, recently introduced by Roychoudhuri (2007). We consider the case of homogeneous and isotropic bodies and present a solution of the Galerkin-type of field equations. The solution is then used to determine the effects of concentrated loads and heat sources in an unbounded medium. The fundamental solutions of the field equations in case of steady vibrations are also derived.     

THERMOELASTICITY OF NONSIMPLE MATERIALS

A linear theory of thermoelasticity for nonsimple materials is derived by using an entropy production inequality proposed by Green and Laws. A uniqueness theorem, complete solutions of the field equations, a study of the plane waves and fundamental solutions for steady vibrations are presented. A method to reduce the thermoelastostatic plane strain problem to an isothermal one is established. The thermal stress problem for an elastic space with a spherical cavity is also considered.     

Computation of practical flow problems with release of latent heat

Practical flow problems with condensation due to phase change from water vapor to water liquid are numerically investigated. Fundamental equations solved in this study consist of conservation laws of mixed gas, water vapor, water liquid, and the number density of water droplets, coupled with the momentum equations and the energy equation. The classical condensation theory is employed for modeling homogeneous nucleation and nonequilibrium condensation. Heterogeneous nucleation is approximately modeled by assuming a constant radius and a constant number density of droplets. These equations are solved by a high-order high-resolution finite-difference method. As external flows, condensate transonic flows around NACA0012 airfoil in atmospheric flow conditions are calculated, and as internal flows, steady and unsteady transonic wet-steam flows through a steam turbine cascade channel are also calculated.     

Fractional Order Theory of Thermoelasticity for Elastic Medium with Variable Material Properties

In this work, a new theory of generalized thermoelasticity for elastic media with variable properties has been constructed in the context of the fractional order heat conduction. The Clausius inequality and the higher expansions of the free energy are used to derive the formulations of anisotropic heterogeneous material with temperature-dependent material properties. The governing equations for the isotropic homogeneous material are also obtained, and which can be reduced to the corresponding L-S theory and the classical coupled theory for the different values of the fractional order parameter, respectively. Furthermore, a uniqueness theorem of the initial mixed boundary value problem for this new theory is stated and proved.     

Fundamental solutions of thermoelasticity with a recent heat conduction model with a single delay term

The present work is concerned with the thermoelasticity theory based on a very recently proposed heat conduction model—a heat conduction model with a delay term introduced by Quintanilla. Here we aim to obtain the fundamental solutions of thermoelasticity in the context of this theory. We derive the solution of Galerkin-type field equations for the case of homogeneous and isotropic bodies. With the help of this solution, we determine the effects of concentrated heat sources and body forces in an unbounded medium. We further obtain the fundamental solutions of the field equations in case of steady vibrations.     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

Method to derive thermoelastic Green’s functions for cylindrical domains

This article presents a new method to derive Green’s functions for boundary value problems (BVPs) of steady-state thermoelasticity for domains described in cylindrical system of coordinate. The proposed method is based on new integral representations for main thermoelastic Green’s functions (MTGFs) in terms of Green’s functions for incompressible Lamé equations written in a cylindrical system of coordinates. The method is demonstrated on a BVP for cylindrical half-wedge for which MTGFs and Green-type integral formula are derived. The obtained MTGFs for half-wedge are validated by MTGFs for respective BVP for thermoelastic wedge that are obtained earlier using ΘG convolution method (ΘGCM). New MTGFs for octant, quarter-space, and half-space as particular cases of the cylindrical half-wedge also can be easily written. The advantages of the proposed method, called method of incompressible cylindrical integral representations (MICIR), in comparison with ΘGCM, are: (a) it is not necessary to construct influence functions for elastic volume dilatation Θ^(q), caused by unit point body force; and (b) it is not necessary to compute complicated convolution (volume integral of product between Θ^(q) and Green’s function G_T) in heat conduction equation.     

Radial integration boundary element method for heat conduction problems with convective heat transfer boundary

A new boundary domain integral equation with convective heat transfer boundary is presented to solve variable coefficient heat conduction problems. Green’s function for the Laplace equation is used to derive the basic integral equation with varying heat conductivities, and as a result, domain integrals are included in the derived integral equations. The existing domain integral is converted into an equivalent boundary integral using the radial integration method by expressing the normalized temperature as a series of radial basis functions. This treatment results in a pure boundary element analysis algorithm and requires no internal cells to evaluate the domain integral. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method.