由运动内热源引起的磁热黏弹性问题的研究

在具有两个热松弛时间的广义热弹性理论下, 研究了处于定常磁场中的均布各向同性黏弹性半空间中, 由以均匀速度运动的线热源引起的瞬态波问题. 通过引入黏弹性向量势和热黏弹性标量势,问题退化为求解3个偏微分方程. 运用Laplace变换(对时间变量)和Fourier变换(对一个空间变量), 得到了变换域内应力和位移的解析表达式. 采用级数展开法, 得到了边界位移在小时间范围内的近似解, 给出了解的近似范围, 同时还研究了两种特例：(1)热源静止不动, (2)不考虑热松弛时间的影响. 最后对于丙烯酸塑料介质给出了数值结果.     

分数阶广义热弹性理论下中空柱热弹性分析

基于Laplace变换及特征值法,推导并给出了分数阶广义热弹性理论下中空柱内表面作用有热冲击情况的解析解,通过Laplace数值逆变换法求解得到了位移场、温度场、应力场的分布规律。结果表明:特征值法能准确给出Laplace域内方程组的解;分数阶参数对温度场和应力场有较大影响,对位移场影响较小。作为广义热弹性理论的一种推广,在处理热传导问题时,通过分数阶广义热弹性理论进行研究更科学、全面。     

饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程，应用Fourier级数展开和Hankel积分变换，得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解．考虑地基表面透水情形，由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答．给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解．该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础．     

理想导体中具有两个松弛时间的电磁热弹性波

研究处于均布磁场中的理想导体的二维电磁热弹性耦合问题，引入势函数使控制方程转化为3个偏微分方程．运用Laplace变换和Fourier变换得到该问题在变换域内的精确表达式，再通过级数展开和Laplace逆变换法求得在时间较短时的逆变换，得到时间-空间域内问题的解．运用此方法研究了表面受到热冲击的半无限空间问题．给出了电磁热弹性波、膨胀波和横向波传播的速度，并通过数值计算，给出了各个场量的分布图．所得结论与已有的结论一致．     

半无限长压电杆的瞬态热冲击问题

采用具有一个热松弛时间的L－S广义热弹性理论，研究了一维半无限长压电杆在一端受到热冲击时的边值问题。借助拉普拉斯正，反变换技术，在所考虑时间非常短的情况下，对问题进行了求解，得到了压电杆上的位移，压力及温度分布的近似解析解，发现应力及温度分布中分别存在两个阶跃点，并给出了算例。     

坡形加热下的二维广义磁热黏弹性问题研究

运用具有一个热松弛时间的广义热黏弹性理论，研究了处于均布磁场中的二维磁热黏弹 性问题. 运用Laplace变换(对时间变量)和Fourier变换(对于一个空间变量)，得到了变 换域内场量的精确表达式，并把结果应用到表面受到坡形加热的半空间问题. 应用 数值逆变换得到了时间-空间域内场量的解，对丙烯酸塑料 给出场量的响应图. 并把运用广义热黏弹性理论所得的结果与传统热黏弹性理 论及热弹性理论下的结果进行了比较.     

考虑热渗效应的有限热源固结近似解1）

通过建立考虑热渗效应和热流固耦合效应的饱和土体固结方程,研究了无限长圆柱热固结问题. 利用Fourier 和Laplace 变换及其逆变换,给出了热固结问题的解析解;然后对空间内无限长圆柱形热源问题进行研究,得到非等温条件下柱体周围饱和土体温度、孔隙水压力的近似解,并总结其规律,分析了热渗系数、固结系数对温度作用下土体固结的影响.     

考虑热渗效应的有限热源固结近似解

通过建立考虑热渗效应和热流固耦合效应的饱和土体固结方程,研究了无限长圆柱热固结问题.利用Fourier和Laplace变换及其逆变换,给出了热固结问题的解析解;然后对空间内无限长圆柱形热源问题进行研究,得到非等温条件下柱体周围饱和土体温度、孔隙水压力的近似解,并总结其规律,分析了热渗系数、固结系数对温度作用下土体固结的影响.     

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.     

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.      

A thermal-shock problem in magneto-thermoelasticity with thermal relaxation

The one-dimensional problem of distribution of thermal stresses and temperature is considered in a generalized thermoelastic electrically conducting half-space permeated by a primary uniform magnetic field when the bounding plane is suddenly heated to a constant temperature.The Laplace transform technique is used to solve the problem. Inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time.Nurnerical computations for two particular cases are carried out.     

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.     

Response of welded thermoelastic solids to the rapid motion of thermomechanical sources parallel to the interface

The analysis of rapidly-moving thermomechanical surface sources is extended to the study of buried thermomechanical sources that move parallel to the interface of two welded dissimilar thermoelastic half-spaces at a constant subcritical speed. The sources are manifest as body force line loads in the coupled equations of thermoelasticity, and a 2-D steady-state situation is treated. Exact integral transform solutions are obtained, and expressions for the displacements and temperature changes are generated by analytical inversion of robust asymptotic versions of the transforms.These expressions show that thermoelastic coupling effects increase with source speed, and that the thermal source is always manifest in combination with a component of the mechanical source, i.e. an effective thermal source term exists. The expressions also exhibit component functions that are in effect hybrids of functions that are seen in purely thermal and isothermal elastic solutions.The critical source speed is defined as the minimum of the two asymptotic thermoelastic Rayleigh speeds in the half-spaces and, when it exists, the asymptotic thermoelastic Stoneley speed. Exact expressions for these speeds are given, and used to present some typical values.     

Mechanical loads on a generalized thermoelastic medium with diffusion

The disturbance caused by the application of continuous mechanical source on the free surface of a homogeneous, isotropic elastic half space in the context of the theory of generalized thermoelastic diffusion with one relaxation time parameter is investigated in the Laplace-Fourier transform domain for a two dimensional problem using eigenvalue approach. The integral transforms are inverted by using a numerical technique. The expressions for displacement components, stresses, temperature field, concentration and chemical potential so obtained in the physical domain are computed numerically and illustrated graphically at different times, for copper like material. As a special case the effect of diffusion on various expressions has also been obtained analytically and depicted graphically.     

The three-dimensional steady-state thermo-elastodynamic problem of moving sources over a half space

A procedure based on the Radon transform and elements of distribution theory is developed to obtain fundamental thermoelastic three-dimensional (3D) solutions for thermal and/or mechanical point sources moving steadily over the surface of a half space. A concentrated heat flux is taken as the thermal source, whereas the mechanical source consists of normal and tangential concentrated loads. It is assumed that the sources move with a constant velocity along a fixed direction. The solutions obtained are exact within the bounds of Biot’s coupled thermo-elastodynamic theory, and results for surface displacements are obtained over the entire speed range (i.e. for sub-Rayleigh, super-Rayleigh/subsonic, transonic and supersonic source speeds). This problem has relevance to situations in Contact Mechanics, Tribology and Dynamic Fracture, and is especially related to the well-known heat checking problem (thermo-mechanical cracking in an unflawed half-space material from high-speed asperity excitations). Our solution technique fully exploits as auxiliary solutions the ones for the corresponding plane-strain and anti-plane shear problems by reducing the original 3D problem to two separate 2D problems. These problems are uncoupled from each other, with the first problem being thermoelastic and the second one pure elastic. In particular, the auxiliary plane-strain problem is completely analogous to the original problem, not only with regard to the field equations but also with regard to the boundary conditions. This makes the technique employed here more advantageous than other techniques, which require the prior determination of a fictitious auxiliary plane-strain problem through solving an integral equation.     

Rolling without Slip on a Transversely Isotropic Thermoelastic Half-space

Rolling without slip by a rigid cylinder on a transversely isotropic, coupled thermoelastic half-space at constant subcritical speed is studied. The cylinder is of infinite length, surface heat convection is neglected, and a dynamic steady state of plane strain is treated. The unmixed problem of traction applied to a translating surface strip is addressed first. A robust asymptotic form of the exact transform solution, valid when Fourier heat conduction dominates any thermal relaxation effect, is extracted, and inverted analytically. Use of material characterization and identification of parameters that vanish in the isotropic limit or are invariant under an isothermal–thermoelastic transformation result in compact full-field solutions. These expressions are used to construct analytical solutions that satisfy the mixed boundary value problem and auxiliary conditions of rolling contact. For the hexagonal material zinc, calculations are made for contact zone width and temperature increases near onset of zone yield. Mathematics Subject Classifications (2000) 73B30, 73C25, 73C30, 73C35.     

Two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source

In this work, a problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity thermally shocked at its bounding surface and subjected to moving heat source with constant velocity has been solved. The governing equations are taken in the context of two-temperature generalized thermoelasticity theory (Youssef model). The analytical solution with direct approach in the Laplace transforms domain has been obtained. The derived analytical expressions have been computed for specific situations. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are represented graphically with comparisons by one-temperature generalized thermoelasticity (Lord–Shulman model).     

State-space approach to thermoelastic interactions in generalized thermoelasticity type III

The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is illustrated with the help of different graphs of numerical values of the field variables.     

Numerical and analytical study of the propagation of thermoelastic waves in a medium with heat-flux relaxation

The thermoelastic problem of laser exposure of metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally.