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。     

无限长圆柱体中广义电磁热弹耦合问题研究

基于L-S广义热弹性理论,研究了处于磁场中无限长理想圆柱导体在边界受热冲击作用时的电磁热弹耦合问题.建立了广义电磁热弹耦合的有限元方程,为避免积分变换方法求解带来的精度丟失.采用将有限元方程直接在时间域求解的方法,得到了圆柱体中的温度、位移、应力、感应磁场和感应电场的分布规律,反映了热的波动性及电磁热弹的耦合效应.结果表明,将有限元方程直接在时间域求解,可以获得各物理量的准确分布.得到温度在热波波前处的阶跃,准确地反应热波的波动效应.     

属性与温度相关材料的广义热弹性问题有限元分析

计及材料特性与温度的相关性,基于Lord和Shulman(L-S)广义热弹性理论,建立了此类问题的有限元控制方程. 由于材料属性的温度相关性,温度控制方程具有非线性,积分变换求解方法难以采用,因而将有限元方程直接在时间域求解. 利用所建立方法研究了材料特性与温度相关、带有孔洞的无限大体在热冲击和机械冲击作用下的广义热弹性问题. 分析表明,在时间域直接求解材料属性与温度相关的广义热弹性问题是可行的,所得结果具有很高的精度,热的波动性得到充分的展现. 同时发现,热冲击载荷作用时,材料属性与温度的相关性对结构的机械响应影响显著,对温度响应影响很小;机械载荷作用时,材料参数与温度的相关性对所有响应影响都很小. 因此,研究热冲击载荷作用的机械响应时,必须考虑材料属性的温度相关性,而研究温度响应时,无论何种冲击载荷,都可以不考虑材料属性的温度相关性.      

超短激光脉冲加热薄板的广义热弹扩散问题

由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.      

半无限粘弹杆的广义磁热粘弹问题

应用Lord-Shulman(L-S)和Green-Lindsay(G-L)广义热弹性理论,研究了在磁场中受移动热源作用的半无限长均质各向同性粘弹杆的磁热粘弹动态响应,并与经典耦合理论进行了对比.给出了杆的广义磁热粘弹耦合的控制方程,借助拉普拉斯积分变换及其数值反变换对控制方程进行了求解,计算得到了杆内温度、应力和位移的分布规律.研究结果表明:时间、热源移动速度和磁场大小对以上分布规律都有一定的影响.     

与温度相关的非均质圆筒的非线性耦合广义热弹性分析

基于能量守恒方程和L–S广义热弹性理论,借助状态空间技术和Newmark法求解了材料性质沿径向任意梯度分布同时又与温度相关的非均质圆筒非线性耦合广义热弹性问题。通过对材料性质与温度无关和相关功能梯度圆筒的算例分析,给出了在线性和非线性耦合下圆筒内温度和应力沿径向和随时间的变化关系,验证了本文解的正确性和有效性。数值结果表明,考虑材料性质是否与温度相关,能量守恒方程中耦合项是线性还是非线性,得到的温度与应力均存在不同程度的差异。本文解可方便地应用于不同边界条件和初始条件下圆筒的广义热弹性分析。     

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。     

短脉冲激光加热分数阶导热及其热应力研究

短脉冲激光加热引起材料内部复杂的传热过程及热变形,现有的以Fourier定律或Cattaneo-Vernotte松弛方程结合弹性理论为框架建立起来热应力理论在刻画其热物理过程存在严重缺陷. 本文基于分数阶微积分理论, 以半空间为研究对象, 建立了分数阶Cattaneo热传导方程和相应的热应力方程, 给出了问题的初始条件和边界条件, 采用拉普拉斯变换方法, 给出了非高斯时间分布激光热源辐射下温度场和热应力场的解析解, 研究了短脉冲激光加热的温度场及热应力场的热物理行为. 数值计算中, 首先对理论解进行数值验证, 然后取分数阶变量$p=0.5$研究温度场和热应力场的变化特点及激光参数对温度和热应力的影响,最后数值计算分数阶参数对温度和热应力场的影响. 计算结果表明, 分数阶Cattaneo传热方程和热应力方程描述的温度和热应力任然具有波动特性,与经典的Fourier传热模型和标准的Cattaneo传热模型相比, 分数阶阶次越大, 热波波速越小, 热波波动性越明显; 反之, 则热波波速越大, 热扩散性越强.激光加热和冷却的速度越快, 温度上升和下降的速度越快, 压应力和拉应力交替变化越快, 温度变化幅值越小, 热应力幅值影响不明显.      

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...     

A GENERALIZED THERMOELASTIC DIFFUSION PROBLEM OF THIN PLATE HEATED BY THE ULTRASHORT LASER PULSES 1)

由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.     

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.     

Wave propagation in dual-phase-lag anisotropic thermoelasticity

The present paper is concerned with the propagation of plane waves in a transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The governing equations are solved in x–z plane to show the existence of three plane waves. Reflection of these plane waves from thermally insulated as well as isothermal stress-free surfaces is studied to obtain a system of three non-homogeneous equations in reflection coefficients of reflected waves. For numerical computations of speeds and reflection coefficients, a particular material is modeled as transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The speeds of plane waves are computed numerically for a certain range of the angle of propagation and are shown graphically against the angle of propagation for the cases of dual-phase-lag (DPL) thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity. Reflection coefficients of various reflected plane waves are computed numerically for thermally insulated as well as isothermal cases and are shown graphically against the angle of incidence for the cases of DPL thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity.     

一维半无限压电杆的广义的热冲击问题

采用具有两个热松驰时间的G－L广义热弹性理论，研究了一维无限无限长杆在其端部受到热冲击时的边值问题，借助于拉普拉斯正、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。得到了位移及温度分布的近似妥析角，发现位移及温度分布中分别存在两上阶跃点，并通过数值计算，把温度的分布规律用图形反映了出来，从温度的分布图上可以看出，当任何x的值大于第二个阶跃点的位置值时，温度值都是零，也即在当前所绘定的时刻，热以波的形式沿压电杆仅传播到第二阶跃点的位置，而在第二个阶跃点之后，压电杆上的温度分布保持初始温度；定不同时刻，热波波前的位置也将相应的在压电杆上移动，也即热波波前在压电杆上的位置随考虑时刻不同而不同，这与经典的热传导是完全不同的，它说明热是以波的形式以有限的速度，而不是以无限的速度在介质中进行传播的。     

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.     

Memory response on thermal wave propagation in an elastic solid with voids

Abstract

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite porous material subjected to the presence of distributed time-dependent heat source acting over the plane area. The heat transport equation for this problem is involving the memory dependent derivative on a slipping interval in the context of three-phase-lag (3PL) model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature, stress, and displacement are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative and delay time also.

Communicated by Nickolay Banichuk.     

物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性,基于Clausius不等式和L-S广义热弹性理论,通过对自由能公式的高阶展开,构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组,利用热冲击的瞬时特征,借助于Laplace正、逆变换技术及其极限性质,给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例,得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响,但值得注意的是,相比于位移场和应力场的显著影响,其对温度场的影响效果并不明显。     

A state space formalism and perturbation method for generalized thermoelasticity of anisotropic bodies

A state space formalism for generalized anisotropic thermoelasticity accounting for thermomechanical coupling and thermal relaxation is developed, which includes the classical thermoelasticity as a special case. By properly grouping the field variables using matrix notations, the basic equations of thermoelasticity are formulated into a state equation and an output equation in terms of the state vector. To obtain the solution for a specific problem it suffices to solve the state equation under the prescribed conditions. For weak thermomechanical coupling an asymptotic solution can be obtained by using the method of perturbation with multiple scales. Propagation of plane harmonic thermoelastic waves in an anisotropic medium is studied within the context.     

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.