不同理论下广义压电热弹性问题的有限元求解

基于G-L和L-S广义压电热弹性理论研究了无限大厚压电板在上下表面受到条带状热冲击时的广义压电热弹性问题。在时间非常短的情况下，为避免积分变换求解带来的精度丢失，采用有限元方法对问题在时间域进行直接求解，获得压电板在热冲击作用下的温度、位移、应力及电势等，并将结果与经典压电热弹性理论进行比较。结果表明，直接求解方法可以准确描述热在介质中以有限的速度传播。     

Free vibration of microstretch thermoelastic plate with one relaxation time

The propagation of waves in microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Lord and Shulman (L–S) theories of thermoelasticity. The secular equations for both symmetric and skew-symmetric wave mode propagation have been obtained. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation. The amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew symmetric wave modes are computed analytically and presented graphically for different theories of thermoelasticity. The theoretical and numerical computations are found to be in close agreement.     

Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.     

Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time

The present paper is aimed at studying the effect of rotation on the general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I Crack problem considered. The problem is in the context of the generalized thermoelasticity Lord-?hulman??s (L-S) theory with one relaxation time, as well as the classical dynamical coupled theory (CD) The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories.     

激光脉冲加热的二维广义热弹性问题研究

基于L-S广义热弹性理论,研究了半无限大板局部受到激光脉冲加热时的广义热弹性问题.为避免常规积分变换方法求解带来的精度丢失,采用有限元法直接在时间域进行求解,得到了激光脉冲加热时板中的温度、位移及应力的变化规律.结果表明,直接求解方法可以准确描述热在介质中以有限的速度传播,同时发现,激光脉冲加热过后,结构的最高温度随着时间的推移逐渐降低,且最高温度的位置总在热波波前附近,此处的应力也明显高于其他区域.     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method

In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic elements under magnetothermal load to meet special engineering requirements. An erratum to this article can be found at     

A Dual Phase Lag Model on Thermoelastic Interaction in an Infinite Fiber-Reinforced Anisotropic Medium with a Circular Hole

The model of generalized thermoelasticity proposed by dual phase lag (DPL), is applied to study the thermoelastic interactions in an infinite fiber-reinforced anisotropic medium with a circular hole. A decaying with time thermal field on the boundary of the hole, which is stress free, causes the thermoelastic interactions. The solutions for displacement, temperature, and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress, and displacement are studied. The exact solution in the case of isotropic medium is discussed explicitly. The accuracy of the finite element method validated by comparing between the finite element and exact solutions for absence the reinforcement.     

Effect of magneto-thermo-viscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation

The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement, temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very pronounced on displacement, temperature and stresses.     

磁_微极广义热弹性介质中轴对称变形的弹性动力学

The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.     

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman 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 coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.     

瞬态热冲击下层合材料板界面的热弹性行为

基于带有两个热松弛时间的G-L广义热弹性理论, 利用有限元方法研究了零阻抗理想界面层合板在瞬态热冲击诱导的位移、应力和温度等通过界面时的热弹性行为. 通过比较不同层中材料的比热容、热导系数、热松弛时间和密度等对界面处的位移、应力和温度的影响, 研究了不同材料参数对复合材料热力学行为影响, 发现不同材料参数将导致热穿过界面时界面处温度、位移和应力发生突变, 研究结果可以为由热引起的层合板挠曲变形提供理论依据.      

直接有限元法求解广义磁热弹二维旋转问题

为了验证直接有限元法求解广义磁热弹耦合旋转问题的有效性及准确性,该文基于Lord和Shulman(L-S)广义热弹性理论,采用直接有限元方法,求解了置于磁场中的旋转半无限大体受热冲击作用的动态响应问题.文中给出了L-S型广义磁热弹耦合旋转问题的控制方程,建立了L-S型广义磁热弹旋转问题的虚位移原理,推导得到了相应的有限...     

Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity

Thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity are studied. The cavity surface is subjected to ramp-type heating of its internal boundary, which is assumed to be traction free. Lord–Shulman and Green–Lindsay models for the generalized thermoelasticity theories are selected since they allow for second-sound effects and reduce to the classical model for an appropriate choice of the parameters. The temperature, radial displacement, radial stress, and hoop stress distributions are computed numerically using the finite-element method (FEM). The results are presented graphically for different values of the thermal relaxation times using the three different theories of generalized thermoelasticity. Excellent agreement is found between the finite-element analysis and analytical and classical solutions.     

Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times (i.e., the G-L theory) are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced magnetic field at the heat wave front and the magnitude of the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.The project supported by the National Natural Science Foundation of China (10132010 and 10472089)The English text was polished by Yunming Chen     

ELECTRO-MAGNETO-THERMOELASTIC PLANE WAVES IN MICROPOLAR SOLID INVOLVING TWO TEMPERATURES

<正>The model of equations of micropolar generalized magneto-thermoelasticity is introduced within the context of the theory of two temperatures generalized thermoelasticity and we consider a problem of an isotropic homogeneous micropolar medium taking into account the heat effects and allowing the magnetic field effects.A plane wave analysis is employed to obtain the exact formulas of the two temperatures(conductive and mechanical),displacement components, micro-rotation components,stresses,couple stresses,induced electric current,electric field and magnetic field.Arbitrary application is chosen to enable us to get the complete solution.The considered variables are presented graphically and discussions are made for the results.     

DYNAMIC RESPONSE OF TWO-DIMENSIONAL GENERALIZED THERMOELASTIC COUPLING PROBLEM SUBJECTED TO A MOVING HEAT SOURCE

Based on the Lord and Shulman generalized thermoelasticity theory with one relaxation time, an isotropic semi-infinite plate subjected to a moving heat source has been studied by employing the finite element method directly in time domain, whose distributions of nora dimensional temperature, displacement and stress are illustrated graphically. The results show that the present method is an effective and exact numerical one for solving the thermoelastic coupling problem and is capable of overcoming the defects of traditional integrated transformation and inverse integrated transformation methods. At the same time, the temperature step of the thermal wave front is obtained exactly in contrast with conventional numerical transformation methods.     

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

Effect of rotation on generalized thermo-viscoelastic Rayleigh–Lamb waves

The present paper is aimed at studying the effects of rotation on the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate rotating about the normal to its faces with uniform angular velocity. This facilitates the decoupling of anti-plane/in-plane motion which is not possible, in general. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The formulation is applied according to three theories of the generalized thermoelasticity: Lord-Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. Secular equations are derived for the plate in closed form isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. In the absence of mechanical relaxations (Rotation and viscous effects), the results for generalized and couple theories of thermoelasticity were obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. Finally the numerical solution is carried out for copper material. The function iteration numerical scheme is used to solve the complex secular equations, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The dispersion curves and attenuation coefficients profiles so obtained for symmetric and skew-symmetric wave modes are presented graphically to illustrate and compare the theoretical results in the presence and absence of rotation. The study may be useful in the construction and design of gyroscopes and rotation sensors as well as in the application in diverse fields.     

Comparative asymptotic analysis of coupled and uncoupled thermoelasticity

The asymptotic solution of the three-dimensional dynamic of coupled thermoelasticity problem (with the mutual influence of the strain and temperature fields taken into account) for an isotropic rectangular plate is used to perform a comparative analysis of the results obtained according to this theory and the theory of temperature stresses. The parameters whose values affect the applicability of these theories and of the applied theory used to solve quasistatic problems of thermoelasticity are obtained.