均匀热荷载作用下层合简支梁的弹性力学解

基于二维热弹性力学理论,研究均匀热荷载作用下层合简支梁的弹性力学解.首先导出均匀温度场中满足控制微分方程和两端简支边界条件的单层梁的弹性力学解,然后利用层间界面位移和应力必须连续的条件,递推得到底层梁与顶层梁间的位移和应力关系.最后根据层合梁上下表面的边界条件确定待定系数,带回递推公式得到整个层合梁的应力和位移分布.本文方法的计算结果有很好的收敛性.与有限元软件的结果对照说明了本文方法的精确性.最后,研究了不同的变温对层合简支梁的位移和应力的影响,结果显示每个层间界面在x方向的应力是不连续.随着温度的升高,梁的最大位移相应地增大.温度越高,位移沿厚度变化的速率越大.     

正交异性厚板在任意荷载下的精确解

本文从三维弹性力学方程出发,抛弃任何有关位移或应力分布的假设,导出正交异性体弹性力学问题的状态方程。给出四边简支任意厚宽比的矩形板在任意荷载作用下的控制方程及其精确解。有关数值结果同Reissner理论、Ambartsumyan理论等得出的相应量进行了比较,并评述了Ambartsumyan等理论的不足之处。     

四边简支各向同性矩形厚板的插值矩阵法解

针对强厚度矩形板四边简支情况,论文根据状态变量法思想,基于三维弹性理论基本方程,以3个位移分量及3个应力分量按双三角级数展开,将三维弹性力学控制方程转化为常微分方程边值问题.尽管一些各向异性弹性矩形厚板早已由状态空间法获得分析解,可是各向同性厚板的分析解至今难以获得,因为状态空间解法中特征方程有重根问题而不易于收敛.论文提出采用插值矩阵法直接对常微分方程进行求解,获得各向同性矩形厚板在四边简支边界条件下三维理论的位移和应力解,并与有限元精细结果进行比较,证明了本文解的准确性.     

荷载作用下多孔饱和地基的热-水-力耦合动力响应分析

基于广义热弹性理论,结合达西定律,对Biot波动方程进行修正,研究了一个受到荷载作用的多孔饱和地基的热-水-力多场耦合动态响应问题。建立了多孔饱和地基在荷载作用下的热-水-力耦合模型及控制方程,该模型可退化为热弹性耦合模型。采用正则模态法求解,得到了问题的解析解,讨论了热-水-力耦合模型和热弹性耦合模型的区别,分析了荷载频率变化对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。     

热荷载作用下薄板振动能流的可视化研究

基于振动声强法研究了热荷载作用下矩形薄板中振动能量的传递和分布特性.首先,得到热荷载作用下薄板的振动方程,并详细给出了热荷载作用下薄板振动声强的表达式,可利用模态叠加法求出薄板振动的横向位移.之后,利用流线可视化技术,通过流线图显示出薄板振动时能量流出的位置,能量被吸收的位置和能量的流动路径.最后,通过具体的数值算例分析了热荷载和机械荷载对薄板振动时能量流动的影响,数值模拟表明施加热荷载后会改变机械荷载对薄板中振动能量流动的影响,使振动能量的流动路径发生明显改变,且在不同的热荷载作用下,通过改变机械荷载可以抵消热荷载对振动能量流动的影响.     

功能梯度材料明德林矩形微板的热弹性阻尼

功能梯度材料微板谐振器热弹性阻尼的建模和预测是此类新型谐振器热?弹耦合振动响应的新课题. 本文采用数学分析方法研究了四边简支功能梯度材料中厚度矩形微板的热弹性阻尼. 基于明德林中厚板理论和单向耦合热传导理论建立了材料性质沿着厚度连续变化的功能梯度微板热弹性自由振动控制微分方程. 在上下表面绝热边界条件下采用分层均匀化方法求解变系数热传导方程, 获得了用变形几何量表示的变温场的解析解. 从而将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的偏微分方程. 然后,利用特征值问题在数学上的相似性,求得了四边简支条件下功能梯度材料明德林矩形微板的复频率解析解, 进而利用复频率法获得了反映谐振器热弹性阻尼水平的逆品质因子. 最后, 给出了材料性质沿板厚按幂函数变化的陶瓷?金属组分功能梯度矩形微板的热弹性阻尼数值结果. 定量地分析了横向剪切变形、材料梯度变化以及几何参数对热弹性阻尼的影响规律. 结果表明, 采用明德林板理论预测的热弹性阻尼值小于基尔霍夫板理论的预测结果, 而且两者的差别随着相对厚度的增大而变得显著.      

叠层连续柱壳热应力问题的弱形式研究

建立了弹性力学基本方程的弱形式,从而得到叠层连续柱壳混合状态方程的边界条件放在一起的算子方程,扩大了求解空间,给出叠层连续闭口柱壳在热荷载和机械荷载作用下的解析解。     

内部荷载作用下圆柱形孔洞的动力响应解答

考虑土与衬砌结构的动力相互作用,本文研究了内源荷载作用下,圆柱形孔洞的动力响应问题.将土体和衬砌结构视为弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程.采用拉普拉斯变换,得到土体及衬砌的位移应力的表达式.利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,可确定表达式的未知系数.采用逆拉普拉斯变换的数值方法,给出了问题的数值解.分析了土中圆形衬砌结构的动力响应随土体和衬砌结构参数的变化规律.     

功能梯度热释电材料矩形板的三维精确分析

对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析．根据正交各向异性热释电材料基本方程，导出了功能梯度热释电材料的状态方程．假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布，获得了四边简支、接地和等温的矩形板，在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解．通过算例，分析了在机械荷载、电荷载和热荷载分别作用下，材料性质的不同梯度变化对平板结构响应的影响．所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。     

功能梯度截顶圆锥壳的热弹性弯曲精确解

研究了功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题. 基于经典线性壳体理论推导出了以横向剪力和中面转角为基本未知量的功能梯度薄圆锥壳轴对称变形的混合型控制方程. 假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数连续变化的形式. 然后采用解析方法求解,得到了问题的精确解. 分别就两端简支和两端固支边界条件,给出了圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线,重点分析和讨论了载荷参数与材料梯度变化参数对变形的影响.      

基于厚度法确定小冲杆试验能量转变温度

以A106管材钢为研究对象,进行了小冲杆断裂试验,获得断后试样的最小厚度;在对试样断裂后的变形分析中,建立了试样厚度减薄率与温度的关系,规避了低温试验中载荷和位移测量不准确导致小冲杆能量转变温度不确定的问题。结果表明:基于厚度法可以准确确定小冲杆断裂试验的能量转变温度;小冲杆断裂试验后,试样最薄厚度的减小率与温度曲线关系呈现S型,有上平台、转变区、下平台三个典型区域;根据厚度减薄率与温度曲线关系可以得到小冲杆的能量转变温度。采用厚度法得到的小冲杆断裂试验的转变温度与能量法获得的结果基本一致。     

瓦斯爆炸过程中火焰厚度测定及其温度场数值模拟分析

本文通过实验的方法，探讨了瓦斯爆炸过程中火焰厚度变化特性及其影响因素，并对瓦斯爆炸过程中的温度场变化进行了数值模拟。研究结果表明，障碍物存在时，瓦斯爆炸过程中产生的火焰厚度常常会小于无障碍物存在时所产生的火焰厚度；膜片所处位置对瓦斯爆炸过程中火焰厚度也有重要影响，膜片距离爆炸源较近时，火焰厚度明显增大，瓦斯爆炸后，火焰阵面着附近区域与管封闭端附近区域温度变化较为陡峭，而火焰阵面后一段区域的温度变化较平缓，且火焰阵面附近温度较高，在障碍物附近温度很快上升到最大值，然后温度开始下降。研究结果对指导现场防治瓦斯爆炸，减轻瓦斯爆炸灾害具有一定的指导意义。     

考虑粗糙度和固体颗粒效应的直齿轮跑合瞬态热弹流润滑分析Transient thermal elasto-hydrodynamic lubrication of spur gears in running-in process considering solid particles and surface roughness

建立了含有固体颗粒的弹流数学模型,修正了Reynolds方程,考虑了连续波状粗糙度的影响,对跑合过程中直齿轮轮齿啮合区的弹流润滑进行了数值解算,分析了固体颗粒和粗糙度对压力、膜厚和温度的影响。结果表明,连续波状粗糙度会引起压力和膜厚一定幅度的上下波动,考虑固体颗粒后,压力变大,膜厚减小;颗粒速度越大,膜厚越小,最小膜厚减小,最大温升一定幅度减小,颗粒所在区域的温升减小;粗糙度波长较小时,粗糙度对膜厚较小的接触区引起的温升较大。     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties

A theoretical study of the effect of variable fluid properties on the Blasius and Sakiadis flow with uniform suction at the asymptotic state is presented in this paper. The investigation concerns air and water taking into account the variation of their physical properties with temperature. Velocity and temperature profiles are presented as well as values of the displacement thickness, momentum thickness, shape factor, wall shear stress and Nusselt number for different temperatures of the plate and the ambient fluid. It is found that the nondimensional displacement thickness, momentum thickness, shape factor, absolute wall shear stress and Nusselt number are identical in both Blasius and Sakiadib flow at the asymptotic state for a fluid with constant properties. The same is valid for any fluid with variable properties if the temperature boundary conditions are the same in Blasius and Sakiadis flow.     

运行过程中载荷突变时可倾瓦推力轴承瞬态热效应的实验研究

研究了可倾瓦推力轴承在名义转速分别为2000r/min和4000r/min下,当载荷突然变化时推力轴在油膜温度和油膜厚度的瞬态变化规律。实验结果表明：当载荷突然增大时,油膜温度以及进油边温度上升,油膜厚度减小;随着载荷变化幅度的增大,温度上升幅度也增大,油膜厚度进一步减小;在载荷变化相同的情况下,相同时间间隔内转速高时油膜温度增大幅度比转速低时要大,而油膜厚度减小幅度比低转速下小。     

Thermal buckling of imperfect functionally graded plates

Thermal buckling analysis of rectangular functionally graded plates (FGPs) with geometrical imperfections is presented in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading as uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect FGP. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.     

Photothermoelastic study of stress concentrations in a plate with internal heating

This paper describes a photothermoelastic method for simulating, in a three-dimensional model, the temperature gradients that occur in structural parts subjected to internal heating such as is frequently encountered in certain areas of nuclear-reactor design. The method is applied to a plate which has a step change in thickness and sustains a nonlinear temperature gradient through its thickness. The shapes of the gradients simulate internal heating of the plate material. The values for the highest stresses on the free surfaces of the plate, within the thickness of the plate, and at the root of the step are presented in graphical form for a range of internal heat-generated conditions. Thermal-stress-concentration factors are presented for a step change in the thickness of a plate under this type of heating. Its design significance is discussed. The same stress and stress-concentration values are shown to also apply to nonnuclear problems. During shut-down in conventional thermal plants, when the walls sustain linear steady-state temperature drops across their thicknesses, temperature profiles exactly analogous to those presented in this paper occur. The stresses can then be computed from the values presented here.     

换向持续时间和换向点位置对往复运动齿轮齿条弹流润滑的影响

往复运动齿轮齿条的润滑失效通常发生在换向死点位置附近，因此研究齿轮齿条换向点位置和换向持续时间对换向过程中润滑油膜的影响具有重要的实际意义。根据齿轮齿条换向瞬间的运动几何关系，建立了换向过程齿轮齿条弹流润滑的瞬态数值模型。采用Ree-Eyring润滑流体，应用多重网格法和多重网格积分法等数值方法，计算得到了齿轮齿条往复运动过程中换向点位置附近一对啮合轮齿间的压力、膜厚和温度，并与前人的实验结果进行了对比验证。分析了不同换向持续时间和换向点位置对一对啮合轮齿间压力、膜厚和温度的影响。齿轮齿条换向过程中油膜厚度明显降低，缩短换向持续时间虽然可以增大齿轮齿条的润滑膜厚，但会导致瞬间油温升高，因此换向持续时间存在最优值。通过比较不同换向死点位置的膜厚发现，当换向死点在单齿啮合后的双齿啮合区时，啮合轮齿间具有较理想的润滑膜厚。无论换向持续时间长短，润滑膜厚的最小值都在换向死点位置，换向死点位置是往复运动齿轮齿条润滑失效的危险点。研究结果为往复运动齿轮齿条的润滑设计提供了理论依据。