基于分数阶热弹性理论的含有球型空腔无限大体的热冲击动态响应

基于新近提出的分数阶广义热弹性理论,研究了含有球型空腔的无限大体受热冲击作用时的动态响应。该文给出分数阶广义热弹性理论下的控制方程,通过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,得到了带有球型空腔无限大体中的无量纲温度、位移、径向应力和环向应力等物理量的分布规律。计算中重点研究了分数阶参数对各物理量的影响效应。结果表明:含有球腔的无限大体内由于热冲击而出现了热弹耦合效应;分数阶参数显著地影响各物理量的分布规律。     

有限元法求解广义热弹耦合一维热冲击问题

为了避免积分变换方法在求解Lord-Shulman(L-S)型广义热弹性耦合问题时由于数值反变换所引起的计算精度降低的问题,该文应用直接有限元方法,求解了基于L-S型广义热弹性理论的窄条薄板受热冲击作用的动态响应问题,结果表明,该方法对求解L-S型广义热弹性耦合的一维问题具有很高的精度。该文给出了L-S型广义热弹性理论下的热弹耦合的控制方程,建立了L-S型的广义热弹性问题的虚位移原理,推导得到了相应的有限元方程。计算得到了窄条薄板中无量纲温度、无量纲位移及无量纲应力的分布规律,从温度分布图上可以清晰地观察到热波波前的特有属性,即热波波前处存在明显的温度梯度的突变。     

分数阶热弹性理论下中空黏弹性圆柱热弹耦合动力响应EI北大核心CSCD

基于Ezzat型分数阶广义热弹性理论,引入Kelvin-Voigt黏弹性模型建立了黏弹性中空圆柱热弹耦合动力模型,探讨了黏弹性中空圆柱热弹耦合问题。中空圆柱体内外表面均有一定约束,且在其外表面处施加热冲击作用。给出Ezzat型分数阶双相滞后广义热弹性理论下问题的控制方程,结合Laplace变换和数值反变换技术对控制方程进行求解,最终得到中空圆柱中无量纲位移、温度、径向应力和环向应力的分布规律,并分析了黏弹性松弛时间因子和分数阶系数对各物理量的影响。结果表明:黏弹性松弛时间因子对于无量纲温度外的所有物理量均有明显影响,但对径向应力和环向应力的影响更为明显;分数阶系数对于所有物理量均有明显影响,在曲线峰值或谷值处影响最显著。     

旋转半无限大体广义电磁热弹性耦合的二维问题

基于广义热弹性理论,研究了热和电可导的旋转半无限大体在其表面受随时间变化的热作用的广义电磁热弹性耦合的二维问题。半无限大体置于恒定的磁场中,受热作用产生膨胀变形,由于外加磁场的作用,介质中产生了感应的电场和感应的磁场。该文建立了电磁热弹性耦合的控制方程,利用正则模态法求解,得到了问题的解析解,并给出了各物理量的分布规律。可以看出,介质中呈现出电磁热弹耦合效应,由于旋转,位移和应力的幅值有很明显的降低,而旋转对温度和感应的磁场的影响不大。     

岩土颗粒介质非等温—维热固结特性研究

基于饱和多孔介质热-水-力完全耦合的控制方程,通过有限Fourier变换及其逆变换,对一维热弹性固结模型进行解析求解,给出土柱内部温度、孔压和位移演化过程的解析表达式。在定义了热固结时间因素和热固结系数等概念的基础上,对非等温条件下饱和土体的热固结特性及其机理进行研究,讨论了土的热固结系数与热扩散系数之比、不同的外力荷载和温度荷载组合等因素对热体积膨胀效应与热固结效应两者耦合作用的影响。此外,还分析了土体热膨胀或收缩对温度演化过程的耦合影响。     

核废料地质处置概念库HM耦合和THM耦合过程的二维离散元分析与比较

描述了二维离散元程序UDEC4.0中求解热-水-应力耦合问题的主要的理论背景、控制方程和计算原理,并假定一座核废料处置概念库位于具有二组节理且赋存地下水的岩体中,使用UDEC程序对处置库近场分别为水-应力耦合及热-水-应力耦合的过程进行了数值模拟,考察和对比了两种工况下坑道围岩中的位移、主应力、塑性区、温度、节理开度、水压力和流速的分布及温度随时间的变化。结果表明,热-水-应力耦合与水-应力耦合相比,核废料放热使得处置库有水围岩中应力、位移的大小和方向发生明显的变化,并且围岩中节理开度、水压力和水流速度均有所减小,特别是在坑道边墙附近相当显著。若要在裂隙岩体中安全、可靠地设计、建造和运行核废料处置库,进行相关的热-水-应力耦合过程的分析是很重要的。     

热耗散变形下螺旋槽干气密封微尺度气膜流动特性研究

螺旋槽干气密封在高压、高速旋转时内部会产生一定量的热,导致密封环发生热弹变形,从而对密封性能产生影响。首先在速度滑移边界条件下,求出螺旋槽内的气膜压力和气膜速度,然后推导出气膜的无热耗散能量方程及有热耗散能量方程,进而利用气膜的压力、速度和能量方程,通过 Maple 和 Matlab 软件求解槽内气膜的温度分布。然后由热弹变形理论,求解出密封环的变形量,获得螺旋槽内气膜厚度的解析式。最后利用广义雷诺方程求出理论泄漏量,并与泄漏量的实验值进行比较。研究结果表明:随着气体从外径流入内径,槽内温度的分布规律是先升高后降低,槽根部周围温度较高;热弹变形量与温度变化的规律一致,而气膜厚度的变化趋势与之相反;干气密封中的泄漏量随变形量增大而增大,考虑热耗散有变形的泄漏量更接近于实验值。     

非均匀温度场压杆蠕变屈曲分析

本文分析了受短时热冲击压杆在非均匀温度场下的蠕变屈曲问题。控制方程考虑了几何非线性以及横截面上应力分布非线性，以内力和位移为基本未知量，在空间上以样条配点法离散，而对时间以初应力法求蠕变变形。计算结果得到了蠕变屈曲破坏的典型模式。     

载流球台薄壳的热磁弹性分析

在轴对称载流薄壳的几何方程、物理方程、运动方程和电动力学方程基础上,建立了载流薄壳热磁弹性耦合方程。考虑电磁场的焦耳热效应,引入热平衡方程及广义欧姆定律得到了薄壳的温度场。应用变量代换进行变形,整理成含有八个基本未知函数的标准柯西型方程式。通过差分及准线性化方法,变换成能用离散正交法编程求解的准线性微分方程组。对于载流球台薄壳,得到了洛仑兹力的表达式,并且推导得到了温度场积分特征值。讨论了载流球台薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对板壳的应力、应变、温度的控制。     

基于热弹性耦合理论的功能梯度材料薄壁旋转碟片力学性能

基于热弹性耦合理论,对处于热载荷下的Al-Al₂O₃功能梯度材料（FGM）薄壁旋转碟片进行研究。根据FGM构造理论结合碟片轴对称特性,得到其力学特性全场分布。分别采用函数构造方法和热耦合传导方程推导得到模型所处温度场,并加以分析对比。建立了统一温度场的热耦合本构方程,并根据平面应力情况下热弹性材料力学特性基本原理,拟合确定其物性系数。通过微分求积方法（DQM）求解不同温度场下不同FGM构造形式模型的位移控制方程。结果表明:常温下,热耦合本构方程可以退化到胡克定律;经典热弹性理论与热弹性耦合理论下的碟片径向位移误差可达41.7%;热弹性耦合理论的结果随温度非线性变化,这种变化趋势也体现在大量科学实验中;碟片外表面温度变化、转速和所处的温度场显著地影响其热弹性场。      

The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity

The transient thermo-piezoelectric response of a functionally graded piezoelectric rod subjected to a moving heat source is investigated in the context of fractional order theory of thermoelasticity proposed by Sherief. The material properties of the functionally graded piezoelectric rod are assumed to vary exponentially along the length, except for the thermal relaxation time and the specific heat, which are taken to be constant. To solve the governing equations of the problem, Laplace transform is applied, eliminating the time effect; the analytical solutions of the displacement, stress, temperature, and electric field in Laplace domain are obtained. Subsequently, the solutions of the considered variables in time domain are obtained by numerical Laplace inversion and illustrated graphically. In calculation, the effect of the fractional order parameter on the variations of the considered variables is presented.     

State space approach to one-dimensional thermal shock problem for a semi-infinite piezoelectric rod

The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one-dimensional semi-infinite piezoelectric rod with its left boundary subjected to a sudden heat. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. Approximate small-time analytical solutions to stress, displacement and temperature are obtained by means of the Laplace transform and inverse transform. It is found that there are two discontinuous points in both stress and temperature solutions. Numerical calculation for stress, displacement and temperature is carried out and displayed graphically.     

Dynamic response of a generalized piezoelectric-thermoelastic problem under fractional order theory of thermoelasticity

The dynamic response of a piezoelectric-thermoelastic rod made of piezoelectric ceramics (PZT-4) subjected to a moving heat source is dealt with in the context of the fractional order theory of thermoelasticity. The piezoelectric-thermoelastic governing equations for the problem are formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered nondimensional temperature, displacement, stress, and electric potential are obtained and illustrated graphically. The effects of fractional order parameter and the velocity of heat source on the variations of the considered variables are investigated, and the results show that they have significant influence on the variations of the considered variables. The present investigation could be helpful for better understanding the multi-field coupling effect of mechanical, electric, and thermal fields in real piezoelectric ceramics structures, and provide some guidelines in the optimal design of actuators or sensors made of piezoelectric ceramics serving in a thermoelastic environment.     

Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent

The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to deal with a thermoelastic–piezoelectric coupled two-dimensional thermal shock problem of a thick piezoelectric plate of infinite extent by means of the hybrid Laplace transform-finite element method. The generalized thermoelastic–piezoelectric coupled finite element equations are formulated. By using Laplace transform the equations are solved and the solutions of the temperature, displacement and electric potential are obtained in the Laplace transform domain. Then the numerical inversion is carried out to obtain the temperature, displacement and electric potential distributions in the physical domain. The distributions are represented graphically. From the distributions, it can be found the wave type heat propagation in the piezoelectric plate. The heat wavefront moves forward with a finite speed in the piezoelectric plate with the passage of time. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in media.     

超急速传热过程中热弹性响应的解析分析

考虑超急速传热过程中诱发的热冲击效应,基于L-S广义热弹性理论,建立了温度突变加热条件下热弹性响应的控制方程组。借助于Laplace正逆变换,在适当简化的条件下推导了一维超急速传热问题热弹性响应的解析表达式。通过对温度场、位移场及应力场的解析求解,给出了超急速传热过程中热波和热弹性波在弹性体内的传递规律,并指出在超急速传热条件下,由于热波和热弹性波的相互叠加作用削弱了热作用产生的热冲击效应。     

Impulsive effect on an elastic solid with generalized thermodiffusion

The theory of generalized thermoelastic diffusion with one relaxation time is employed to study the distribution of temperature, displacement components, stresses, concentration and chemical potential in a semi-infinite medium having an impulsive mechanical load at the origin. Using the joint Laplace and Fourier transforms, the governing equations are transformed into a vector–matrix differential equation which is then solved by the eigenvalue approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace and Fourier transforms. Results of this work are presented graphically and are compared with the results of generalized thermoelasticity and classical elasticity deduced as special cases.     

Thermal shock problem in generalized thermo-viscoelasticty under four theories

A model of the equations of generalized thermoviscoelasticity for isotropic media is given. The formulation is applied to the generalized thermoelasticity theories: Lord-Shulman, Green-Lindsay and Chandrasekharaiah and Tzou as well as to the dynamic coupled theory. The state space approach is adopted for the solution of one-dimensional problems in the absence of heat sources. The Laplace-transform technique is used. The expansions of the stress component, the temperature and the displacement in Laplace transform domain, in power series and the exact inversions for arbitrary time are given. The jump discontinuities are calculated for the four theories. Numerical results are given and illustrated graphically employing numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.     

A unified generalized thermoelasticity solution for the transient thermal shock problem

A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.     

Model of Fractional Heat Conduction in a Thermoelastic Thin Slim Strip under Thermal Shock and Temperature-Dependent Thermal Conductivity

The present paper paper, we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved. Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of order α is applied to obtain a solution. We assumed that the strip surface is to be free from traction and impacted by a thermal shock. The transform of Laplace (LT) and numerical inversion techniques of Laplace were considered for solving the governing basic equations. The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique. The numerical results for the physical variables were calculated numerically and displayed via graphs. The parameter of fractional order effect and variation of thermal conductivity on the displacement, stress, and temperature were investigated and compared with the results of previous studies. The results indicated the strong effect of the external parameters, especially the time-fractional derivative parameter on a thermoelastic thin slim strip phenomenon.     

A note on axisymmetric thermoelastic interactions in an unbounded body with cylindrical cavity

Summary Thermoelastic interactions in a linear, homogeneous and transversely isotropic unbounded body containing a cylindrical cavity due to a time-dependent stress or temperature applied to the boundary of the cavity are studied. A unified system of governing equations that includes among its particular cases the governing equations of the conventional and generalized thermoelasticity theories is employed. By the use of the Laplace transform technique, discontinuities experienced by the temperature, displacement, radial stress and hoop stress fields at the wavefronts are computed under a small-time approximation. Comparison with the corresponding results obtained in earlier work is made.