热冲击荷载作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

在带两个松弛时间参数的广义热弹性线性理论(Green和Lindsay理论)意义上,研究含一个球形空腔的功能梯度球形各向同性无限大弹性介质中,热弹性位移、应力和温度的求解方法.空腔表面无应力,但承受一个随时间变化的热冲击荷载作用.在Laplace变换域中,给出了一组矢量-矩阵微分方程形式的基本方程,并用特征值方法求解.应用Bellman方法进行数值逆变换.计算了位移、应力和温度,并给出相应的图形.结果表明,材料热物理性质的变化,对荷载响应的影响非常强烈.并与对应的均匀材料进行了比较和分析.     

考虑热-水-力耦合效应的饱和多孔地基动力响应分析

基于广义热弹性理论,结合Darcy(达西)定律,对Biot波动方程进行了修正,研究了一个受到椭圆余弦波作用的,均质各向同性半无限大饱和多孔地基的热-水-力多场耦合动态响应问题.建立了饱和多孔弹性地基的热-水-力耦合动力响应模型及控制方程,采用正则模态法求解,得到了问题的解析解,分析了地基中渗透系数变化和椭圆余弦波频率变化对饱和多孔地基中各物理量的影响.最终,给出了无量纲的竖向位移、超孔隙水压力、竖向应力和温度等物理量的分布规律.     

任意梯度分布功能梯度圆环的热弹性分析

对沿径向任意变化的材料参数的功能梯度圆环进行了热弹性分析.与以前关于该问题的分析不同,既不需要预先给定具体的梯度变化形式,也不需要对结构进行细分.给出一种新的有效解法将问题转换为求解Fredholm积分方程,从而通过Fredholm积分方程的解给出热应力和位移的分布情况.最后通过算例分析了内外表面受不同温度作用时,材料参数呈现梯度变化对圆环的应力和位移变化的影响,计算结果表明某些特定的材料梯度可有效缓解圆环内的热应力分布.该文得到的结果对功能梯度圆环在结构安全设计方面有重要的理论指导意义.     

热辐射对粘性流体流过多孔非线性收缩平面时的MHD流动和热传导的影响

研究热辐射对多孔非线性收缩平面上磁流体动力学(MHD)流动和热传导的影响.假设收缩平面的速度和横向磁场,按离原点距离的幂函数而变化;又假设粘性按与其有关的温度的反函数变化,热传导率按温度的线性函数变化.通过广义相似变换,将偏微分方程的控制方程,简化为耦合的非线性常微分方程,然后通过有限差分法进行数值求解.在不同的参数取值下,得到速度和温度分布,以及多孔平面上表面摩擦因数和热传导率的数值结果.     

分数阶热弹理论下重力场对二维纤维增强介质的影响

基于Sherief等提出的分数阶广义热弹性耦合理论，研究了在热冲击作用下二维纤维增强弹性体的热弹性问题.考虑了重力对二维纤维增强线性热弹性各向同性介质的影响，建立了控制方程.运用正则模态法，经过数值计算，对控制方程进行求解，得到了不同分数阶参数和不同重力场下无量纲温度、位移和应力分量的表达式，以图形的方式展示了变量的分布规律并对结果展开了讨论.研究结果为:重力场和分数阶参数对纤维增强介质的位移及应力有着重要的影响，但对温度的影响有限.     

热弹性动力学耦合问题的微分代数方法

对一般的热机械问题提出了一种有效的数值方法,并对二维的热弹性问题进行了测试．该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶,使之成为一组微分代数方程,应力应变关系被写成代数方程．所得到的微分代数系统采用全隐式的向后差分公式进行求解．对该方法进行了详细的说明．为了验证该方法的有效性,将其应用于一个动态非耦合的热弹性问题的求解和一个耦合的二维热弹性问题的求解．     

部分植被化复式河道水流的二维解析解

运用涡粘模型理论对部分植被化复式河道的水流水深平均流速和边壁切应力分布进行了求解.通过对水流微元体进行纵向受力分析建立相应的控制微分方程,其中植被对水流的影响归结为拖曳力项.同时将复式渠道划分为3个子区域,通过联立求解各区域微分方程中的定解系数,最终得到均匀流的条件下各区水深平均流速的横向分布的解析解.在获得水深平均流速的横向分布后,可进一步给出对泥沙输移有重要影响的河床切应力的横向分布.通过与试验测得的资料比较,表明给出的解析解能够为工程设计提供足够精度的水力特性的预报.     

热环境中粘贴压电层功能梯度材料梁的自由振动

研究了上下表面粘贴压电层的功能梯度材料Euler-Bernoulli梁在升温及电场作用下的屈曲和自由振动行为.在精确考虑轴线伸长基础上,建立了压电功能梯度材料层合梁在热-电-机载荷作用下的几何非线性动力学控制方程.其中,假设功能梯度材料性质沿厚度方向按照幂函数连续变化,上下压电层为各向同性均匀材料.在小振幅和谐振动假设下,上述非线性偏微分方程组被转化为两套相互耦合的常微分方程组,即过屈曲问题的控制方程和过屈曲构形附近的线性振动控制方程.采用打靶法数值求解上述两个耦合的常微分方程边值问题,获得了在均匀电场和横向非均匀升温场作用下两端固定压电.功能梯度材料层合梁在屈曲前和过屈曲构型附近的自由振动响应.绘出了梁的过屈曲平衡路径以及前3阶固有频率随热、电载荷及材料梯度参数变化的特性曲线.结果表明,梁的前3阶频率在屈曲前随着温度升高而减小,在进入过屈曲后它们却随着温度升高而增加.通过施加电压在压电层产生拉应力可有效地提高粱的热屈曲临界载荷,从而提高其固有频率.     

黏性流体与热弹性微极蜂窝结构介质界面上受倾斜荷载作用时的弹性动力分析

研究倾斜荷载作用在黏性流体与热弹性微极蜂窝结构固体界面上时,荷载倾斜角的影响.假设倾斜荷载是法向荷载和切向荷载的线性组合.为求解该问题,对时间变量进行Laplace变换,对空间变量进行Fourier变换.通过引入势函数,获得了变换域中应力、温度分布和压力的表达式.利用数值逆变换技术,求得问题的物理解.同时,得到了频域中的表达式,以及变量适当变化时稳态情况下的表达式.用图形显示不同荷载源和荷载倾角变化时的响应.并且讨论了一些特殊情况.     

功能梯度材料Timoshenko梁的热过屈曲分析

研究了功能梯度材料Timoshenko梁在横向非均匀升温下的热过屈曲．在精确考虑轴线伸长和一阶横向剪切变形的基础上,建立了功能梯度Timoshenko梁在热-机械载荷作用下的几何非线性控制方程,将问题归结为含有7个基本未知函数的非线性常微分方程边值问题A·D2其中,假设功能梯度梁的材料性质为沿厚度方向按照幂函数连续变化的形式．然后采用打靶法数值求解所得强非线性边值问题,获得了横向非均匀升温场内两端固定Timoshenko梁的静态非线性热屈曲和热过屈曲数值解．绘出了梁的变形随温度载荷及材料梯度参数变化的特性曲线,分析和讨论了温度载荷及材料的梯度性质参数对梁变形的影响．结果表明,由于材料在横向的非均匀性,均匀升温时的梁中存在拉-弯耦合变形．     

Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes

Stability of a functionally graded (FG) micro-beam, based on modified couple stress theory (MCST), subjected to nonlinear electrostatic pressure and thermal changes regarding convection and radiation, is the main purpose of this paper. It is assumed that the functionally graded beam, made of metal and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as an exponential function through its thickness. By changing the ceramic constituent percent of the bottom surface, five different types of the micro-beams are investigated. The static pull-in voltages in presence of temperature changes are obtained by using step-by-step linearization method (SSLM) and, by adapting Runge–Kutta approach, the dynamic pull-in voltages are obtained numerically. Though the temperature distribution through the thickness of FG micro-beam (due to its too small measurement) is considered uniform, owing to the different thermal expansions of layers, temperature changes cause deflection in the micro-beam, and consequently affect pull-in values. Hence the profound effects of different material constituent over the pull-in voltages are illustrated and it is graphically displayed that how in some cases neglecting components of the couple stress leads to inaccurate results.     

轻质热防护系统波纹夹芯结构热力耦合分析

高超声速飞行器在出入大气层或持续在空间飞行时,将遭受严苛的气动加热载荷．对热防护系统进行传热分析是进行热力耦合分析的基础,而温度分布的特点直接影响到波纹夹芯结构的热应力等问题．首先对一体化热防护系统（integrated thermal protection system, ITPS）进行隔热性能分析,得到整个结构的温度场;然后采用顺序耦合的数值方法,模拟分析ITPS波纹夹芯结构单胞的热力耦合性能,给出波纹夹芯结构在静力载荷以及热力耦合载荷条件下的应力场、位移场,并对计算结果进行了讨论．结果表明波纹夹芯结构在初始尺寸及约束条件下,只满足在高温热流作用下飞行器低压区使用,而当气动压力大于等于15 000 Pa时,结构将发生破坏．     

陶瓷/金属功能梯度材料圆筒的热应力分析

对金属-功能梯度材料-陶瓷的三层组合圆筒进行了热应力分析,导出了定常温度分布及热应力分布的计算表达式,并就ZrO₂/Ti-6Al-4V梯度材料的热应力进行了计算和讨论.     

Progressive thermal stress distribution around a crack under Joule heating in orthotropic materials

Stress intensity factor and stress distribution at crack tips are classical problems in solids, which are closely related to the failure and reliability of materials. A crack in a nonlinearly coupled anisotropic medium, on the other hand, is much more difficult to analyze. Using the generalized complex variable method, the thermal stress problem of a crack embedded in an orthotropic medium has been analyzed, and the progressive thermal stress distributions have been obtained in closed-forms. The analysis shows that the thermal stress intensity factors are linear functions of remote thermal flux while are nonlinear functions of remote current; the thermal stress distributions under produced by thermal flux and Joule heating are similar, but not identical; the thermal stress intensity factors are linear functions with respect to the thermal expansion coefficients; with the increase of crack length, the thermal stress intensity factor caused by Joule heat increases rapidly; the thermal stress intensity factors are directly proportional to the temperature difference between the upper and lower crack surfaces and the left and right half crack surfaces divided by the square root of the crack length, and the ratios are only determined by the material parameters. These results provide a powerful tool for the failure and reliability analysis of conductive materials, and suggested that thermal stress analysis may be localized.     

Finite element modeling of welding processes

This work deals with the simulation of fusion welding by the Finite Element Method. The implemented models include a moving heat source, temperature dependence of thermo-physical properties, elasto-plasticity, non-steady state heat transfer, and mechanical analysis. The thermal problem is assumed to be uncoupled from the mechanical one, so the thermal analysis is performed separately and previously to the mechanical analysis at each time step. The mechanical problem is based on the thermal history. A special treatment is performed on mechanical elements during the liquid/solid and solid/liquid phase changes to account for stress states. The three-dimensional stress state of a butt-welded joint is obtained as an example of an application.     

Effect of memory dependent derivative on forced transverse vibrations in transversely isotropic thermoelastic cantilever nano-Beam with two temperature

The present research deals with the study of forced vibrations in transversely isotropic thermoelastic (TIT) nanoscale beam with two temperature (2T). Memory dependent derivative theory of thermoelasticity for clamped-free/cantilever nano-beam has been considered. The mathematical model is prepared for the nanoscale beam in a closed form with the application of Euler Bernoulli beam theory. Laplace transform method is employed to solve the problem. Forced vibrations due to exponential decaying time varying load acting vertically downward along the thickness direction of the nano-beam, Uniform load, Time harmonic load have been considered. Dynamic analysis for these forced vibrations and Static analysis has been carried out in this research. The dimensionless expressions for lateral deflection, thermal moment, temperature change, and axial stress are solved for these three forced vibrations. Response ratio has also been calculated. The analytical results have been numerically analysed using programming in MATLAB. The effect of kernel function has been depicted graphically on the lateral deflection, thermal moment, temperature change, axial stress and response ratio for all the three types of forced vibrations. Some particular cases have also been discussed.     

On a symplectic analytical singular element for cracks under thermal shock considering heat flux singularity

In a precise numerical modelling of cracks under thermal shock, the singularity issue resulted from heat flux should also be considered in addition to the one resulted from stress. The assumptions of constant temperature distribution usually adopted in the existing studies may lead to significant error. The concerned problem involves the discretization in both space and time domains. Numerical error resulted from the singularity issues in the space domain may be accumulated in the time domain. Hence, a unified framework which integrates reliable methods for both space and time domains are desired. In the present contribution, the classic thermal stress problem is restudied under the Hamiltonian system and the eigen functions are obtained analytically. A symplectic analytical singular element (SASE) for thermal stress analysis is reformulated based on the existing ones for thermal conduction and stress analyses. The singularity issues of both stress and heat flux are considered. A unified framework is formed with the precise time domain expanding algorithm (PTDEA) for the time domain and the formulated SASE for the space domain. A self-adaptive technique is used for the PTDEA to improve the numerical efficiency. The time dependent fracture parameters i.e., heat flux intensity factors (HFITs) and the mixed mode thermal stress intensity factors (TSIFs) can be solved accurately without any post-processing. Numerical examples are given for verification and validation of the proposed method.     

A fully-coupled nonlinear thermoelectromechanical model for piezolaminated smart structures

In present engineering applications piezoelectric materials gain increasing importance in the development of smart structures; e.g., for shape and vibration control problems. Such structures exhibit a three-way coupling effect between the mechanical, electrical and thermal quantities. In the majority of papers available in literature this coupling is taken into account only in the constitutive equations. It is however well known that truly coupled analysis should also be based on the interaction of the mechanical, thermal and electrostatic quantities in the field equations. Only in this way many physical effects can be taken into account; e.g., the strain rate dependant change of temperature due to mechanical loading. Furthermore most of the analyses conducted in this area are performed in the linear range of deformations assuming small strains, rotations and temperature changes. However smart technology is generally applied to thin walled structures and in many cases reported in literature the deflections are much larger than the thickness, which results into geometrically nonlinear behaviour, like e.g. the occurrence of stress stiffening which greatly affects the prediction of sensor voltage outputs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Couple stress fluid flow with variable properties: A second law analysis

The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.     

Thermal alternation induced vibration analysis of spacecraft with lateral solar arrays in orbit

The rigid-flexible-thermal coupling dynamic analysis for a spacecraft in orbit is studied in this paper. The spacecraft consists of a central rigid platform and two groups of lateral solar arrays. There exists the relative motion between the rigid platform and solar arrays, thus the spacecraft is a multi-rigid-flexible bodies coupling system. As the spacecraft in orbit experience different light areas, alternations of the heat flux on solar arrays can result in changes of dynamic characteristics. Considering thermal stress effects of solar arrays, the dynamical model of the spacecraft is established by using Hamiltonian principle. Further, multi-rigid-flexible coupling modes of the system are obtained. The finite difference method is developed to obtained the responses of the spacecraft and the variation of temperature gradients under the different solar radiation. Results of natural characteristics illustrate that constrained modes can be used to discrete the system directly and efficiently. Modal shapes and parameters analysis reveal the rigid-flexible coupling effects of such spacecraft. The thermal-structural analysis demonstrates the thermal alternation may induce the vibration and even change the original vibration of the spacecraft.