机械荷载与热荷载共同作用下变厚度梁的热弹性力学解

本文研究了两端简支变厚度梁受机械荷载与热荷载共同作用下的热弹性力学解.温度场用调和级数展开,通过求解热传导方程可首先确定温度沿梁厚度方向的非线性分布情况.从二维热弹性力学理论的基本方程出发,导出满足控制微分方程和两端简支边界条件的位移函数的一般解,对上下表面的边界方程作傅立叶正弦级数展开确定待定系数,数值结果与商业有限元软件ANSYS进行了比较,显示出很高的精度.本文方法可直接应用于对应力和位移分析要求较高的工程问题,如航空航天和微型机械的设计.     

A COORDINATE TRANSFORMATION METHOD FOR NUMERICAL SOLUTIONS OF TRAVELING-WAVE ELECTROOMTIC FLOWS IN MICROCHANNEL

采用坐标变换法数值求解了耦合的Poisson-Nernst-Planck（PNP）方程和Navier—Stokes（NS）方程,研究二维狭窄微通道行波电场电渗流数值解．数值结果表明,坐标变换法能有效降低电渗流解数值解在双电层的高梯度,有效改善数值解的收敛性和稳定性．坐标变换的电渗流数值解和原始坐标下的数值解完全一致．坐标变换后采用简单的网格也能得到和原始坐标下复杂网格相同的解．给出了滑移边界的近似解与完整的PNP—NS数值解的比较．在双电层厚度与微通道深度比值（λ／H）很小的情况下（相对深通道）,两者的解基本一致．但在λ／H较大时（相对浅通道）滑移边界的解高于电渗流速度．     

坐标变换法数值求解微通道行波电场电渗流

采用坐标变换法数值求解了耦合的Poisson-Nernst-Planck (PNP)方程和Navier-Stokes(NS)方程, 研究二维狭窄微通道行波电场电渗流数值解. 数值结果表明,坐标变换法能有效降低电渗流解数值解在双电层的高梯度, 有效改善数值解的收敛性和稳定性. 坐标变换的电渗流数值解和原始坐标下的数值解完全一致. 坐标变换后采用简单的网格也能得到和原始坐标下复杂网格相同的解. 给出了滑移边界的近似解与完整的PNP-NS数值解的比较. 在双电层厚度与微通道深度比值(λ/H)很小的情况下(相对深通道), 两者的解基本一致. 但在λ/H较大时(相对浅通道)滑移边界的解高于电渗流速度.      

反对称斜交叠层板双向弯曲问题的横向基理论解

研究反对称斜交叠层板的双向弯曲问题。根据横向基理论，在厚度方向，给出了三个方向位移沿厚度的分布规律；在面内方向，采用升阶谱位移函数；然后，应用最小势能原理导出叠层板的静力控制方程。通过对多种层数和铺层角的层板力学响应计算分析表明：在典型位置的应力分布，本文解与三维弹性解符合很好，并有较好的收敛性。     

裂纹端部细短纤维的应力分析

基于裂纹端部存在与其裂纹面相垂直的二相细短纤维分析模型，采用叠加原理推导了求解纤维表面应力分布函数的积分方程，通过简化得到了该方程的解析表达显式，该积分方程的特征值方程是纤维几何参数，材料常数以及纤维相对于裂纹位置的相关函数，当材料参数不满足特征方程时，积分方程将具有唯一解；并借助数值方法，给出了纤维剪应力分布算例，和纤维对应力强度因子的影响。     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义，本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式，此方法将Roe型熵稳定格式与自适应移动网格算法结合，空间方向采用熵稳定格式对磁流体动力学方程进行离散，利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布，在此基础上采用守恒型插值公式实现新旧节点上的量值传递，利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明，该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高，通用性好，具有强鲁棒性。     

基于格子Boltzmann模型的SINE-GORDON方程的数值解法

我们给出了用于求解Sine-Gordon方程的格子Boitzmann模型．通过假设与时间导数有关的平衡态分布函数，得到了具有2阶误差的Sine-Gordon方程的格子Boitzmann算法．数值例子再现了在零点附近的扭结解。     

焊接残余应力平板多个共面表面裂纹的应力强度因子

采用线弹簧模型求解含焊接残余应力平板多个共面任意分布表面裂纹的应力强度因子.利用边裂纹权函数给出了裂纹表面上沿厚度非线性分布的残余应力向线性分布的转化公式.基于Reissner板理论和连续分布位错思想,将含多个共面任意分布表面裂纹的无限平板问题归结为一组Cauchy型奇异积分方程,并采用Gauss-Chebyshev方法获得了奇异积分方程的数值解.以三共面表面裂纹为例,计算了表面裂纹的应力强度因子,并讨论了裂纹间距、裂纹几何形状等因素对应力强度因子的影响.     

梯度材料中矩形裂纹的对偶边界元方法分析

采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解,以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上,面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解,采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比,建议方法可以获得高精度的计算结果. 最后,分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子,讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响.      

非平面应变状态下的叠层厚壁筒

抛弃任何有关位移或应力模式的人为假设，在轴对称情况下，导出正交异性厚壁筒的状态方程。在沿筒轴方向任意分布的轴对称荷载下，给出叠层厚壁筒静力问题的精确解。此解满足所有弹性力学基本方程，包含了全部弹性常数，可满足任意精度要求。数值结果和ＳＡＰ５有限元解进行了对比。     

触变性流体在旋转圆盘上的流动

采用甩涂过程的基本方程，导得触变性流体在旋转圆盘上流动的速度分布．并利用特征线法，得到薄膜厚度的方程．对其定性分析表明，流体的重建系数越小和破坏系数越大，将加快甩涂过程．     

Casson流体在旋转圆盘上的流动

本文研究Casson流体在旋转圆盘上的涂层流动特性,得到基本流动的速度分布,并且用Runge-Kutta法进行数值计算,得到薄膜厚度随时间和流态参数的变化规律,还用能量法检验了流动稳定性。     

Analysis of functionally graded rotating disks with variable thickness

Elastic solutions for axisymmetric rotating disks made of functionally graded material with variable thickness are presented. The material properties and disk thickness profile are assumed to be represented by two power-law distributions. In the case of hollow disk, based on the form of the power-law distribution for the mechanical properties of the constituent components and the thickness profile function, both analytical and semi-analytical solutions are given under free–free and fixed-free boundary conditions. For the solid disk, only semi-analytical solution is presented. The effects of the material grading index and the geometry of the disk on the stresses and displacements are investigated. It is found that a functionally graded rotating disk with parabolic or hyperbolic convergent thickness profile has smaller stresses and displacements compared with that of uniform thickness. It is seen that the maximum radial stress for the solid functionally graded disk with parabolic thickness profile is not at the centre like uniform thickness disk. Results of this paper suggest that a rotating functionally graded disk with parabolic concave or hyperbolic convergent thickness profile can be more efficient than the one with uniform thickness.     

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier-Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.     

Biaxial flexural strength distribution of thin ceramic substrates with surface defects

The statistical models of the strength of thin ceramic substrates with surface defects under piston-on-3-ball loading conditions are formulated using Batdorf’s statistical theory and Kirstein and Woolley’s moment equations. These models possess the form of a Weibull distribution function, making it possible to process the piston-on-3-ball biaxial flexural strength data using a Weibull treatment. During this study, it was noted that the thickness of the specimen had no effect on the failure distribution. Therefore, it was deemed that a reasonable thickness of the specimen disk could be selected for the piston-on-3-ball test in the case where the thickness is so small that the deflection of the center of the specimen exceeds half of the thickness (this thickness would invalidate the strength evaluation equation specified in ASTM F 394-78). The strengths of seven different compositions of 8YSZ with dopants were tested using the piston-on-3-ball method. The results were then processed using the derived models. The failure distributions of the different thickness groups of 8YSZ specimens were similar, verifying that the thickness, indeed, has no effect on the failure distribution.     

粘弹性流体在旋转圆盘上的流动

利用线性Maxwell模型,研究了粘弹性流体在旋转圆盘上的流动．并应用摄动法：求得涂层厚度的近似解析解．发现增加涂料的弹性,有助于甩涂．     

Equi-strength design of nonhomogeneous variable thickness high speed rotating disk under steady temperature field

Considering the mutual interaction between the thickness ofthe disk and temperature distribution, and directly using results in [1].[2] and the iteration method stage sied in this paper, we obtain the equi-strength thickness distribution of nonhomogeneous variable thickness high speed rotating disk under axisymmetrieal steady temperature field.Projects Supported by the Science and Technic Fund of the National Education Committee     

Flow of a Casson fluid on a rotating disk

The flow of a thin layer of a Casson fluid on a fast rotating disk is considered. The film thickness distribution at various times for various initial thickness distribution is calculated. The stability of the flow is examined.     

串列风力机尾流干扰的研究简

广义致动盘方法是通过引入体积力代替叶片的致动盘技术与三维Navier-Stokes 方程相结合来获得风力机周围流场信息的一种方法. 该方法避免了花费大量网格与计算资源去求解风力机叶片的附面层,从而可以把更多的网格与计算资源用于风力机尾流流场的模拟,非常适合用于风力机尾流流场的研究. 以NH1500风力机为计算模型,将常规CFD (computational fluid dynamics) 方法与广义致动盘方法计算所得的叶片载荷分布进行比较,以验证广义致动盘方法的可行性. 然后使用广义致动盘方法对风场中串列风力机进行数值模拟,研究串列风力机之间间距变化时,上游风力机产生的尾流对下游风力机的干扰影响.     

STEADY HEAT CONDUCTION OF A DISC WITH NON-HOMOGENEITY AND VARIABLE THICKNESS

In this paper, we use the stepped reduction method suggested by Yeh Kal-yuan in 1965 to obtain the general oslution of steady heat conduction of a disc with nonhomogeneity and variable thickness. Through an illustrative example, the error of Yeh's method is analysed. The result shows that it is effective for solving ordinary differential equation with variable coefficients.