TEC结构的三维非线性瞬态温度场分析

热电制冷器(TEC)以其体积小、作用速度快及无噪音等机械制冷无法替代的优点在航空航天和电子工业等领域得到了越来越广泛的应用。本文根据TEC的导热特点,推导了TEC结构稳态温度场的解析解,建立了其瞬态非线性温度场分析的微分方程。利用伽辽金法导出TEC结构热分析的有限元方程,对非线性热分析的有限元方程进行了求解,得到了TEC的稳态温度场和瞬态响应温度场。算例结果表明,本文提出的TEC结构热分析有限元模型具有较高的精度,能够有效地分析TEC的非线性瞬态温度场。     

空间薄壁管结构瞬态温度场、热变形有限元分析

对于辐射换热的薄壁杆件航天结构，为分析其在太空中不同时刻的姿态下的温度场和热变形，构造了一种相对自由度矩形管单元。其基本思想是从2维非线性瞬态热传导方程出发，假设沿矩形管横截面上每边的温度为线性分布，用4个角点的平均温度和温差来表示矩形管横截面上的温度分布，构造了一种1维2结点温度杆单元，该单元每个结点包含平均温度，上下面温差，左右面温差3个自由度；在计算热变形时，此三个广义温度参数分别对应热轴力和2个热弯矩载荷。经与三维有限元计算结果的比较，证明用该单元计算的矩形管温度场和位移场是可靠的。利用这种新型的薄壁矩形管单元和本文作者在其他文章中提出的薄壁圆管单元，可以对非线性换热条件下的复杂空间结构进行比较准确的温度场和热变形有限元分析，最后本文计算了考虑遮挡的太阳能帆板的瞬态温度场和热变形以说明其应用价值。     

有限厚度、大压入的球压试验材料力学响应

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题,基于薄壳的几何方程、物理方程、运动方程、电动力学方程,建立其热磁弹性基本方程．应用线性化方法,得到了关于热磁弹性问题的线性迭代方程,转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体,给出Lorentz力表达式,导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律,并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

辐射换热下瞬态热-结构分析的一种空间薄壁杆单元

发展了一种用于辐射换热条件下瞬态热-结构分析的空间薄壁杆单元,其截面形式可以是任意形状的闭口截面和单支开口截面。该单元温度场分解为平均温度和多谐摄动温度,沿杆轴方向采用两结点线性插值,沿杆截面周向用三角函数展开,每结点含多个解耦的自由度,其中结点平均温度方程同传统一维温度有限元方程为非线性,各谐摄动温度方程为线性,然后利用Wilson-θ法求解结构的瞬态温度场。本文选择了两节点Ber-noulli直梁单元得到准静态热弹性有限元方程并求解,针对非对称开口截面考虑了翘曲变形及弯扭耦合的影响。温度场引起的等效热载荷不仅包括常规的热轴力,还包括热弯矩以及热双力矩。本文针对不同截面形式的梁单元给出了瞬态温度场以及热变形的验证算例,并通过与商业程序中二维壳元计算结果的比较说明了本文所提出方法的正确性和高效性。     

太阳强烈辐射对大跨度球面网壳静力性能的影响

在太阳辐射下大跨度建筑物的外部温度场呈非均匀分布,阴面区域的温度低于阳面区域的温度.均匀温度场和非均匀温度场假定给出的分析结果不同.外部温度场受太阳辐射、风速、涂层材料及周围物体辐射反射率等因素的影响.采用简化方法实现大跨度空间钢结构在太阳辐射下外部温度场模拟,得到一个地区的球面网壳外部温度场的分布规律.使用有限元法分析外部非均匀温度场对网壳结构受力性能的影响.算例分析表明,均匀温度分布假定不适用于大跨度双层球面网壳结构的设计.     

有限长FGM圆筒的热/机应力的解析解

利用微分方程的级数求解方法,分析了两端简支的有限长功能梯度圆筒的轴对称稳态热弹性问题,推导出了稳态温度场与应力场的解析解。分析中采用指数函数模型来描述FGM圆筒中材料性能在厚度方向的连续变化,同时忽略温度对材料性能的影响。另外,论文以金属钼和多铝红柱石制成的功能梯度圆筒为例,给出了稳态温度场和应力场的数值结果。     

火灾情况下混凝土板温度场的解析解

针对火灾情况下火场温度和构件边界的温度均随时间不断变化的问题,应用杜哈美尔定理分析了边界温度按一定规律随时间变化的热传导问题。推导得到了火灾情况下混凝土板温度场的解析解公式,并应用MATLAB编程计算得到了解析解结果。比较解析解的计算结果和试验结果发现:两者得到的截面温度场都呈非线性分布;两者的变化趋势一致,即近火面的温度梯度很大,距受火面越远,温度梯度越小;温度曲线都是凸向坐标轴。因此,推导得到的解析解公式适合于求解火灾时混凝土板横截面的温度场。同时,只要能够求出非齐次项与时间无关时的辅助问题的解,便可应用杜哈美尔定理求解该热传导问题的温度场,因此该方法可推广应用于火灾情况下其它构件温度场解析解的计算。     

变厚度载流旋转壳体的热磁弹性分析

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题，基于薄壳的几何方程、物理方程、运动方程、电动力学方程，建立其热磁弹性基本方程．应用线性化方法，得到了关于热磁弹性问题的线性迭代方程，转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体，给出Lorentz力表达式，导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律，并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

火灾情况下混凝土板温度场的解析解

针对火灾情况下火场温度和构件边界的温度均随时间不断变化的问题,应用杜哈美尔定理分析了边界温度按一定规律随时间变化的热传导问题。推导得到了火灾情况下混凝土板温度场的解析解公式,并应用 MATLAB 编程计算得到了解析解结果。比较解析解的计算结果和试验结果发现：两者得到的截面温度场都呈非线性分布;两者的变化趋势一致,即近火面的温度梯度很大,距受火面越远,温度梯度越小;温度曲线都是凸向坐标轴。因此,推导得到的解析解公式适合于求解火灾时混凝土板横截面的温度场。同时,只要能够求出非齐次项与时间无关时的辅助问题的解,便可应用杜哈美尔定理求解该热传导问题的温度场,因此该方法可推广应用于火灾情况下其它构件温度场解析解的计算。     

静态受载裂纹尖端附近的温度场

利用理想弹塑性介质中在小范围屈服的条件下静态Ⅲ型裂纹塑性变形的解析解建立了一个热源模型.由这个热源模型得到了裂纹尖端附近温度场的积分表达式.详细研究了温度场和加载速率之间的关系.证明了在快速加载的条件下,裂纹尖端附近的温升有r~(-1)阶的奇异性.当加载速率一定时,求出了裂纹尖端温升的上限的一个简单表达式.给出了温度场的数值计算结果及实际测量结果,其符合程度是令人满意的.     

沿垂等温平板的自然对流问题的近似解析解

本文用加权残值得到了沿垂等温平板的自然对流问题的近似解析解。和已有准确解的比较表明，在平板表面附近，近似解有很好的精度，而且速度场的精度比温度场更好一些。文末还对配域法的准收敛问题作了说明。     

Steady-state heat transfer through a slab-on-ground floor over a constant temperature water table

Explicit analytical solutions are obtained for two-dimensional steady-state heat transfer rate from a slab-on-ground floor over a constant temperature water table. The floor heat transfer rate results calculated using the derived expression are in close agreement with a series expansion solution available in the literature. The current work offers accurate temperature field and floor steady state heat loss calculations for long-narrow slab-on-ground buildings over a water table at finite depth.     

Periodic heat conduction with relaxation time in cylindrical geometry

Steady-periodic heat conduction with relaxation time in an infinitely long hollow cylinder is considered. Four boundary value problems, with boundary conditions of the first and of the second kind, are solved analytically. The solution for a solid cylinder with a sinusoidally varying surface temperature is obtained as a special case of a solution found for the hollow cylinder. The effects of the relaxation time on the steady-periodic temperature field are analysed, in details, for a solid cylinder with a sinusoidally varying surface temperature and for a hollow cylinder with a sinusoidally varying heat flux at the inner surface and with a constant temperature at the outer surface. The results show that thermal resonances may occur and suggest that accurate measurements of the relaxation time could be obtained by means of experiments on steady-periodic heat conduction in cylindrical geometry. Received on 15 April 1997     

Finite element procedures for time-dependent convection–diffusion–reaction systems

New finite element procedures based on the streamline-upwind/Petrov-Galerkin formulations are developed for time-dependent convection-diffusion-reaction equations. These procedures minimize spurious oscillations for convection-dominated and reaction-dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations. As a special application problem, the single-well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests.     

On the Plane Orthotropic Stress Problem of Quasi-Static Thermoelasticity

The plane stress boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using accurate estimation and the contraction mapping principle. Representations of solutions of the field equation are obtained, and some solvability results are proved. The results are of both theoretical and numerical interest.     

On the plane problem of orthotropic quasi-static thermoelasticity

The plane displacement boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using an accurate estimate and the contractive mapping principle. Representation of solution of the field equation is obtained, and some solvability results are proved. The results are of both theoretical and numerical interest.     

用热线风速仪同时测量流场速度与温度

本文对流体力学实验研究中广泛使用的热线风速仪常用的测温和测速方法进行了改进，提出了一种同时测量流场速度与温度的方法。与分时测量相比，此方法具有较高的准确性。因此，本方法将有助于全面分析速度场与温度场的相互影响与关系。     

Non-linear thermal stability of bimetallic shallow shells of revolution

In this paper, a theory for non-linear thermal stability of open bimetallic shallow shells of revolution under a uniform temperature field is developed. To apply the theory to the particular case of some elastic elements in precision instruments, this paper discusses two important kinds of shells, the bimetallic shallow spherical shell with a circular hole at the center and the bimetallic truncated shallow conical shell. The more accurate solutions are obtained by the modified iteration method. All results are expressed in curves which may be applied directly to the design of the elastic elements.     

Determining isoclinics from fringe patterns

A procedure has been developed which imparts new flexibility and increased usefulness to the bonded-polariscope technique. It also may help to increase the precision of the shear-difference method of principal-stress separation by providing greater precision to the determination of principal-stress directions. The procedure involves bonding a uniaxially stress-frozen plate of model material into a model between Polaroid sheets to function as a bonded polariscope. The fringe data obtained under load provide information for determining the principal-stress directions throughout the model by solution of a simple algebraic relation which lends itself readily to accurate plotting for graphical analysis. The inherent precision should exceed that of isoclinic analysis, particularly in regions where indistinct isoclinics might be expected, since accuracy increases with loading. Accurate fringe-order data also can be obtained by plotting fringe order as a function of position. The basis for the procedure is the modification of the applied-stress field by the presence of the residual (frozen)-stress field. Furthermore, the frozen-fringe order combines with the fringes applied at room temperature as though both stress fields were applied at room temperature. Theory and experimental confirmation are presented, together with a sample principal-stress map which is compared with that obtained from theory, and also from isoclinics. In addition, the chart for rapid graphical solution is included.     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。