DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.     

Thermoconductivity and thermoelasticity of thin isotropic shells heated by a moving heat pulse

The paper presents a solution to the problem of thermal conduction and thermoelasticity for a thin shallow spherical shell heated by a concentrated or local impulsive heat source moving over the shell surface. It is assumed that temperature is linearly distributed across the shell thickness and that the shell, on its sides, exchanges heat with the environment in accordance with Newton’s law of cooling. The Fourier and Laplace transforms are used to find an analytic solution. The dependence of the temperature field and stress/strain components on the type of heating and the form of heat source is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 85–92, November 2006.     

层合球面各向同性热释电空心球的瞬态响应

运用叠加原理，将层合球面各向同性热释电空心球的球对称动力学问题的解分成准静态和动 态两部分，准静态部分首先运用状态空间法给出了显式表达式，然后运用分离变量法、初参 数法和特征函数展开技术，给出了动态部分的表示式，再结合内外表面上的电学边界条件和 界面上的电学连续条件，导出一个关于时间函数的第二类Volterra积分方程，运用插值法 可成功地给出此积分方程的高精度数值解，最终可求得原问题的位移、应力、电位移以及电 势的响应. 此方法适用任意层数且各层是任意厚度的层合热释电空心球作用随时间以任意形 式变化的球对称温度场. 文中还给出了数值结果.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric Thermoelastic Interactions without Energy Dissipation in an Unbounded Body with Cylindrical Cavity

The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occurs at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.     

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.     

EFFECTIVE SPECIFIC HEATS OF MULTI-PHASE THERMOELASTIC COMPOSITES

This paper studies the effective properties of multi-phase thermoelastic composites. Based on the Helmholtz free energy and the Gibbs free energy of individual phases, the effective elastic tensor, thermal-expansion tensor, and specific heats of the multi-phase composites are derived by means of the volume average of free-energies of these phases. Particular emphasis is placed on the derivation of new analytical expressions of effective specific heats at constant-strain and constant-stress situations, in which a modified Eshelby’s micromechanics theory is developed and the interaction between inclusions is considered. As an illustrative example, the analytical expression of the effective specific heat for a three-phase thermoelastic composite is presented.     

Spectral analysis and stability of thermoelastic Bresse system with second sound and boundary viscoelastic damping

In this paper, we consider the energy decay rate of a thermoelastic Bresse system with variable coefficients. Assume that the thermo-propagation in the system satisfies the Cattaneo's law, which can eliminate the paradox of infinite speed of thermal propagation in the assumption of the Fourier's law in the classical theory of thermoelasticity. Meanwhile, we also discuss the effect of a boundary viscoelastic damping on the stability of this system. By a detailed spectral analysis, we obtain the expressions of the spectrum and deduce some spectral properties of the system. Then based on the distribution of the spectrum, we prove that the energy of the system with a boundary viscoelastic damping decays exponentially. However, it no longer decays exponentially if there is no boundary damping. Copyright © 2013 John Wiley & Sons, Ltd.     

On the spatial behavior of solutions for non-linear type II heat conduction

In this paper we study the spatial behavior of the solutions for a problem determined by the non-linear version of the Green and Naghdi type II heat conduction theory. We obtain a spatial decay estimates for the usual boundary-initial-value problem and also an upper bound for the amplitude term of the spatial estimate. Finally, we analyze a non-standard initial value problem defined on a particular family of heat conductors.