双圆柱体结构的热耦合微分方程及其有限元解

针对物体的热耦合问题,给出了内外形式的双圆柱体结构的热耦合分析的基本微分方程,提出了采用有限元进行求解的方法,并给出了具体算例.热耦合是一个复杂的多元微分方程的求解问题.求解得知,热应力分布情况不仅与几何形状有关,也与热载荷与材料物理特性有关,在一定温度变化范围内,物体由于温度变化所产生的等效应力会随温度呈近似线性变化.此外,结构几何尺寸对应力分布变化的影响大于对温度分布变化的影响.     

表面效应对热电材料中纳米孔周围热应力的影响

基于完整Gurtin-Murdoch(G-M)低阶表面能模型，进一步探讨了纳米尺度下表面效应的影响.建立了合理考虑构型变化的应力边界条件，实现了研究尺度从宏观到微观的转变.利用复变函数理论和保角映射技术，构建了用于纳米尺度下的热-电-力理论框架模型，得到了热电基体中纳米孔周围热场、温度场以及应力场的半解析解.数值结果表明，相对于完整G-M模型，简化G-M模型(忽略孔洞构型变化的影响)往往会高估表面效应和远场热电载荷对热应力分布的影响.此外，表面效应的存在将在一定程度上缓解纳米孔周围的热应力集中.     

一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题

考虑裂纹内部介质的热传导率,研究了一维六方准晶非周期平面内含中心开口裂纹的平面热弹性问题.利用Fourier积分变换技术,得到了热应力、裂纹尖端处的热应力强度因子和应变能密度因子的封闭解.数值结果讨论了裂纹内部介质的热传导率、外载荷及声子场-相位子场耦合系数对热应力强度因子和应变能密度因子的影响.结果表明,声子场-相位子场耦合系数对裂纹扩展影响较大.当声子场载荷较小或热流密度较大时,裂纹不易扩展,热流密度在裂纹尖端处会出现集中热效应.随着裂纹内部介质热传导率的增大,热流密度逐渐增加而热应力强度因子逐渐减小.该文所得结果为准晶热力学性质的实际应用提供了理论依据,进而可用于优化准晶元器件的设计和制备.     

四段式有限元法分析热耦合的流体-固体相互作用问题

给出了一种流(体)-热-结构综合的分析方法,固体中的热传导耦合了粘性流体中的热对流,因而在固体中产生热应力.应用四段式有限元法和流线逆风Petrov-Galerkin法分析热粘性流动,应用Galerkin法分析固体中的热传导和热应力.应用二阶半隐式Crank-Nicolson格式对时间积分,提高了非线性方程线性化后的计算效率.为了简化所有有限元公式,采用3节点的三角形单元,对所有的变量:流体的速度分量、压力、温度和固体的位移,使用同阶次的插值函数.这样做的主要优点是,使流体-固体介面处的热传导连接成一体.数个测试问题的结果表明,这种有限元法是有效的,且能加深对流(体)-热-结构相互作用现象的理解.     

圆板在局部Gauss温度场作用下的响应分析

基于薄板热弯曲理论,推导了圆板在Gauss(高斯)温度场作用下的挠度和热应力解析表达式,分析了边界条件和局部温度参数对圆板挠度和热应力的影响,为局部温度变化薄板结构的热力学分析提供理论依据.研究结果表明:圆板中心处的挠度和压应力有最大值;在热影响区内,圆板内一点的挠度随着该点到板中心距离的增大呈Gauss型减小趋势;在热影响区外,圆板挠度的变化趋势与圆板边界约束形式和辐照因子有关,辐照因子越大,边界简支圆板挠度越先呈线性减小趋势;圆板挠度的解析解与有限元解一致.在热影响区内,圆板内一点的热应力随着该点到板中心距离的增大呈Gauss型减小趋势,两种边界约束圆板的热应力变化趋势相似;在热影响区外,圆板热应力的变化趋势与圆板边界约束形式和辐照因子有关.     

硅通孔(TSV)的工艺引入热应力及其释放结构设计

在3D SiP(三维系统级封装)的TSV(硅通孔)的工艺制造过程中,热应力会引发TSV周围的载流子迁移率的改变,进而改变3D系统级封装芯片的性能.针对这一问题,提出了一种TSV热应力释放槽结构,以期解决微机电系统(MEMS)应用的大尺寸TSV的热应力问题.在释放槽内外,硅衬底表面的应力得到有效隔离,表面应力大大降低.在结合可行工艺参数的基础上,通过数值模拟对比了3D与2D模型的区别、不同TSV材料的区别,计算应力释放槽的深度、位置、宽度等因素对硅衬底表面应力释放的效果,给出了TSV应力释放槽的布局建议.研究结果表明含有释放槽的TSV,释放槽外热应力可以减小至无释放槽情况下的40%~60%,保留区域的面积也相应降低.     

指数型功能梯度材料平面问题热应力通解

研究了功能梯度材料平面问题的热应力场,首先引入热弹性位移势函数,得到温度场的应力解;然后引入Airy应力函数,通过求解功能梯度材料平面问题的基本方程,得到不考虑温度时的应力,叠加后得到平面问题的热应力通解.     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源.     

固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

变温度荷载作用下半无限成层饱和介质的热固结分析

对半无限成层饱和多孔介质作用随时间变化的温度荷载的热固结问题进行解析求解．其中,热-水-力耦合线性弹性控制方程考虑了热渗效应和等温热流效应的影响．先采用Laplace变换求其在变换域上的解,然后用数值方法求逆变换．对半无限体表面作用呈指数衰减热荷载的双层体系进行研究,分析了两层介质热固结系数、弹性模量等的差异性对热固结特征的影响．研究表明:位移场和应力场对温度场的耦合作用可以忽略,而热渗效应对温度和孔压有显著影响．     

Thermo-magneto-dynamic stresses and perturbation of magnetic field vector in a non-homogeneous hollow cylinder

An analytical method is presented to investigate thermo-magneto-elastic stresses and perturbation of the magnetic field vector in a conducting non-homogeneous hollow cylinder under thermal shock. The interaction between the deformation and the magnetic field vector in a non-homogeneous hollow cylinder is considered by adding a Lorentz’s electro-magneto-force into the equation of thermo-elastic motion of the non-homogeneous hollow cylinder in an axial magnetic field. The exact solution for magneto-thermo-dynamic stresses and perturbation responses of an axial magnetic field vector in a conducting non-homogeneous hollow cylinder was obtained by using finite integral transforms. From numerical calculations, the dynamic characteristics on both thermo-magneto-stresses and perturbation of the axial magnetic field vector in the conducting non-homogeneous hollow cylinder is revealed and discussed.     

微极液体在两个多孔圆盘间的MHD流动及其热传导

两个平行的无限大多孔圆盘,圆盘表面有均匀注入时,数值地研究圆盘间不可压缩导电微极流体,在横向外加磁场作用下的轴对称稳定层流.运用von Krmn的相似变换,将非线性运动的控制方程转化为无量纲形式.使用基于有限差分格式的算法,在相应的边界条件下,求解简化后耦合的常微分方程组.讨论Reynolds数、磁场参数、微极参数和Prandtl数,对流动速度和温度分布的影响.在特殊情况下,所得结果与已有文献的工作有着很好的一致性.研究表明,圆盘表面的传热率随着Rynolds数、磁场参数和Prandtl数的增加而增加;剪切应力随着注入的增加而减少,但它随着外部磁场的加强而增加.和Newton流体相比较,微极流体的剪切应力因素较弱,有利于聚合体加工过程中流动和温度的控制.     

One-dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk

In this paper, the magneto-thermo-mechanical response of a functionally graded magneto-elastic material (FGMM) annular variable-thickness rotating disk is investigated. The material properties namely material stiffness, heat conduction coefficient, thermal expansion coefficient, mass density and magnetic permeability are assumed to vary continuously along the radial direction according to a power law. The thickness profile of the disk placed in a uniform magnetic field and subjected to the thermal load is assumed to be hyperbolic in nature. The effects of the magnetic field, grading index and geometric nonlinearity on the mechanical and thermal stresses of the disk are investigated. For a specific value of the grading index the maximum radial stress due to magneto-mechanical load in a mounted FGMM disk with hyperbolic convergent profile is found away from the center. This result is different from other thickness profile disks where the radial stresses are always at the center. It is observed that unlike radial stress in a mounted FGM disk subjected to mechanical load only where it is always tensile, the radial stress due to magneto-thermal load in a mounted FGMM disk can be both tensile and compressive type. It is seen that a decrease in the value of grading index invokes shifting of the location of the maximum temperature in FGMM disk with hyperbolic convergent profile towards the outer surface of the disk.     

Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software

A hollow sphere made from functionally graded piezoelectric material (FGPM) such as PZT_4 has been considered. One-dimensional analytical method for electro-thermo-mechanical response of symmetrical spheres is used. For asymmetric three-dimensional analysis, ANSYS finite element software is employed in this study. Loading is combination of internal and external pressures, a distributed temperature field due to steady state heat conduction and a constant electric potential difference between its inner and outer surfaces for analytical solution. In three-dimensional solutions closed and open spheres with different boundary conditions subjected to an internal pressure and a uniform temperature field are studied. All mechanical, thermal and piezoelectric properties except the Poisson’s ratio are assumed to be power functions of radius. It has been found from analytical solution that the induced radial and circumferential stresses of an imposed electric potential is similar to the residual stresses locked in the homogeneous sphere during the autofrettage process of these vessels. It has been concluded from the three-dimensional analysis that the magnitudes of effective stresses at all node points are higher for the clamped-clamped boundary condition and are lower for the simply-simply supported condition.     

On dynamic effects in an elastic half-space under “thermal impact” : PMM vol. 38, n 6, 1974, pp. 1105–1113

The general uncoupled dynamical problem of thermoelasticity for a half-space under the condition of a thermal impact with a finite rate of change in temperature on its boundary is solved by the method of principal (fundamental) functions within the framework of a generalized theory of heat conduction.An elastic steel half-space is analyzed as an illustration. The problem on thermal stresses originating in an elastic half-space due to thermal impact produced by a jump change in temperature on the boundary was first analyzed in [1]. Since the temperature change on the boundary occurs at a finite rate, it is generally impossible to realize the thermal impact considered in [1] physically. The dynamic effects in an elastic half-space under a thermal impact with finite rate of change in the temperature on the boundary have been studied in [2]. For high rates of change of the heat flux we obtain a generalized wave equation of heat conduction [3] taking into account the finite velocity of heat propagation. Hence, the solution of the ordinary parabolic heat conduction equation used in [1, 2] does not correspond to the true temperature field. The problems of [1, 2] have been examined in [4, 5], respectively, within the framework of a generalized theory of heat conduction.     

Thermomagnetic convection induced by a time-modulated driving force in magnetic fluids

It is well-known that the flow properties of magnetic fluids – so called ferrofluids – can be modified by applying an external magnetic field. Under certain conditions, the magnetic force induced by this external field causes a convective flow. What has yet to be investigated is what happens when this driving force is modulated in time. For this purpose, a horizontal ferrofluid layer has been exposed to an intermittent magnetic field, which causes a time-modulated force. This force depends on the strength of the external magnetic field and the fluid temperature, and therefore the flow phenomenon generated is called thermomagnetic convection. In addition, if the fluid layer is heated from below, the classical thermal convection contributes to the flow system. In our studies, both effects – thermomagnetic and thermal – contribute together to the convection. The experimental results presented here confirm previous theoretical investigations about the influence of the frequency of the driving force on the strength of the convective flow, which reach minimum values at certain frequencies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

A numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite-difference method

This paper presents the development of the magneto-thermoelastic problem in non-homogeneous isotropic cylinder in a primary magnetic field when the curved surface of the cylinder subject to certain boundary conditions. The governing coupled linear partial differential equations in the hyperbolic-type have been solved numerically using the finite-difference method. Graphical results for the temperature, displacement and components of stresses are illustrated and discussed for copper-like material. The results indicate that the effects of inhomogeneity and magnetic field are very pronounced. Some more interesting particular cases have also been discussed.     

Free convection flow about a cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a vertical down-pointing cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic parameter and the Prandtl number. The results show that the magnetic field suppresses the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.