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调和
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  biharmonic
    Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane
    双解析函数、双调和函数和平面弹性问题
短句来源
    FENG Kang, YU De-hao and some other scholars of our country are the first ones to create the natural boundary element method (NBEM), and they have successfully studied the natural boundary reduction method for the boundary value problems of harmonic equation and biharmonic equation.
    我国学者冯康、余德浩等首创自然边界元法 ,并已成功地研究了调和方程及双调和方程边值问题的自然边界归化方法。
短句来源
    In this paper, the mean value theorem of the solution of a elastic thin plate on Winkler's foundation is given. As a special case, the mean value theorem of a two dimensional biharmonic function is obtained when the coefficient k of the foundation reaction approaches zero.
    本文给出了winkler基础上弹性薄板解的中值定理,作为一个特殊情况,当地基反力系数k趋于零时,获得了二维双调和函数的中值定理
短句来源
    This is a method on the basis of satisfying biharmonic equation of the plate by using principle of minimum complementary energy to result in concordant displacement of plate and frame.
    所用方法是以满足板的双调和方程为基础,运用最小余能原理,达到板与框架的位移协调一致.
短句来源
    The converse theorems of mean value theorem of two and three dimensional biharmonic function are presented and proven
    提出并证明了二维和三维双调和函数中值定理的逆定理
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  “调和”译为未确定词的双语例句
    The Converse Theorems of the Mean Value Theorem of Two and Three Dimensional Biharmonic Function
    双调和函数中值定理的逆定理
短句来源
    THE SOLUTION OF GREEN FUNCTION FOR TWO-HARMONIC EQUATION ON FEBRIC-MECHANIC
    弹性力学平面问题的双调和方程的格林函数解法
短句来源
    In this paper is proposed a boundary collocation technique for evaluating the torsionalrigidity and the third stress intensity factor of cracked bars.
    按照调和函数u(x,y)在裂纹线上的值应为零这一条件作特征展开,而后利用边界配置法,使u(x,y)的边界条件近似满足. 调和函数u(x,y)求出以后,便可以算出抗扭刚度D 和第三型应力强度因子K_Ⅲ.
短句来源
    The leading term solutions for the velocity components v and w also show that the solution consists of two parts: one corresponds to the variation of the section area depending on the solution of a poisson equation, and another corresponds to the variation of the section shape depending on the solution of a Laplace equation with Nuemann type boundary condition.
    横截面上的速度分量可分解为代表截面积的大小变化和形状变化的两部分,其中代表面积大小变化部分的速度分量由文中的简单公式给出,求形状变化部分的速度分量相当于求解一个平面调和函数的Neumann边值问题.
短句来源
    Boundary integral equations are formulated for both elastic and elastoplastic torsion of axisymmetric bodies by the stress function approach.
    本文利用调和函数性质和格林公式,建立以应力函数和边界合剪应力为场变量的边界积分方程.
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  biharmonic
Using the representation of the system of Stokes equations in terms of the stream function in a region including a single periodic element, we obtain a boundary-value problem for the biharmonic operator.
      
Plane-parallel vortex systems in a viscous incompressible fluid in channels with parallel walls and in a corner with no-slip conditions on the walls are investigated on the basis of exact solutions of the biharmonic equation.
      
A computer-based laser system for the selective diagnostics of hydrogen in gas mixtures based on the coherent anti-Stokes Raman scattering (CARS) method using biharmonic pumping on the basis of stimulated Raman scattering (SRS) is developed.
      
It is proved that a function which is biharmonic in a half-strip and satisfies homogeneous Dirichlet conditions at the base of the strip oscillates.
      
Zero radius interaction for the biharmonic and polyharmonic equations
      
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本文用应变能中的变分法得出了自由矩形块体的热弹性应力基本公式。并借助于“实用调和分析法”解出了自由矩形块体对称冷却的热弹性应力結果。

In this paper is proposed a boundary collocation technique for evaluating the torsionalrigidity and the third stress intensity factor of cracked bars.The proposed eigen-functionexpansion form is quite different from Sih's in that it is convenient both for evaluatingthe torsional rigidity and third stress intensity factor.The three cases considered in this paper are the cracked rectangular section,the crackedround section and the cracked angular section.The numerical results for the torsionalrigidity and third...

In this paper is proposed a boundary collocation technique for evaluating the torsionalrigidity and the third stress intensity factor of cracked bars.The proposed eigen-functionexpansion form is quite different from Sih's in that it is convenient both for evaluatingthe torsional rigidity and third stress intensity factor.The three cases considered in this paper are the cracked rectangular section,the crackedround section and the cracked angular section.The numerical results for the torsionalrigidity and third stress intensity factor are shown.

在开裂柱形杆的扭转问题中,取应力函数(?)(x,y)=u(x,y)-y~2,则u(x,y)是一个调和函数.按照调和函数u(x,y)在裂纹线上的值应为零这一条件作特征展开,而后利用边界配置法,使u(x,y)的边界条件近似满足.调和函数u(x,y)求出以后,便可以算出抗扭刚度D 和第三型应力强度因子K_Ⅲ.文中的特征展开形式不同于薛昌明所采用的特征展开形式.本文的特征展开形式和整个计算过程都比较简便.本文计算了:(1)两组开裂矩形截面杆的D 和K_Ⅲ(图3,4,5和6),结果和Westermann的计算结果相同.(2)三组开裂角钢的D 和K_Ⅲ(图8和图9),对于这种截面尚未见算过.(3)四组开裂圆轴的D 和K_Ⅲ(图11和图12),当单侧裂纹垂直于圆截面周边时,薛昌明得到了闭合形式的解,他的解答只能算出裂纹长度小于和等于半径的情况,而本文的数值解法并不受这个限制.当裂纹长度等于半径时,薛昌明所得为K_Ⅲ=0.5469T/R~(5/2),本文所得数值结果为K_Ⅲ=0.5468T/R~(5/2).其他三组,即裂纹和截面周边不垂直的情况,也未见算过.

An approximate solution for flow field in an inlet with curved axis and arbitrary cross section is given in the present paper. The flow in the inlet is assumed to be inviscid, compressible, steady and potential. Also, the inlet is assumed to be a slender one, which means that the scale of the cross section is much less than the scale of the redius of curvature of the inlet axis and the variation of the area and the shape of the cross section along the axis is very small. The coordinate system is taken as follows:...

An approximate solution for flow field in an inlet with curved axis and arbitrary cross section is given in the present paper. The flow in the inlet is assumed to be inviscid, compressible, steady and potential. Also, the inlet is assumed to be a slender one, which means that the scale of the cross section is much less than the scale of the redius of curvature of the inlet axis and the variation of the area and the shape of the cross section along the axis is very small. The coordinate system is taken as follows: The x-axis is along the curved axis of the inlet and pointing downstream, and the y- and z-axes are the local Cartesian coordinates in the plane of local cross section perpendicular to the inlet axis as shown in Fig.1. The inlet axis is considered to be a planar curve in the present paper, and the y-axis is chosen in the plane of inlet axis. A slenderness parameter δ(<< 1) which measures the ratio of the scale of the cross section to the scale of the radius of curvature of the inlet axis is chosen as a perturbation parameter. Then the new coordinates(ξ,η,ζ) defined by Eq.(9) is introduced so that the values of(ξ,η,ζ) are of order of one throughout the flow field. The asymptotic expansions of Eq.(17) in terms of δ are developed for the solution, where φ is the velocity potential, u, v, w are the velocity components along the x-, y-, z-axes, respectively, and ρ is the flow density. The solution to the second term for the axial velocity component u is obtained, which shows that the approximate value of u at the centroid of the cross section is equal to the local one-dimensional value, whereas the value of u at other point of the cross section is inversely proportional to the distance between the point and the center of the local radius of the inlet axis. The leading term solutions for the velocity components v and w also show that the solution consists of two parts: one corresponds to the variation of the section area depending on the solution of a poisson equation, and another corresponds to the variation of the section shape depending on the solution of a Laplace equation with Nuemann type boundary condition.

本文应用摄动法给出了任意截面的弯曲进气道内流场的近似计算方法.进气道内的气体假设是可压缩的无粘性有势流动.进气道的轴线假设是任意的平面曲线,而且截面的形状也可以是任意的.同时还要求进气道的几何形状是细长的,即横截面方向的尺度要比其轴线的曲率半径小得多,而且截面积的大小及形状沿轴线方向的变化是缓慢的.近似解的结果表明,截面积形心处的轴向速度等于按一元流关系算出的值,而非形心处的轴向速度则和该点至轴线曲率中心处的距离成反比.横截面上的速度分量可分解为代表截面积的大小变化和形状变化的两部分,其中代表面积大小变化部分的速度分量由文中的简单公式给出,求形状变化部分的速度分量相当于求解一个平面调和函数的Neumann边值问题.

 
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