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equation     
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  方程
    Superplastic Constitutive Equation for Metal with Fine Grain and Its Application
    金属细晶超塑本构方程及应用
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    A SIMPLE INTEGRAL EQUATION METHOD FOR THREEDIMENSIONAL PROBLEMS OF CYLINDER EMBEDDED IN A HALF-SPACE
    圆柱嵌入半空间的三维问题的一个简便的积分方程解法
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    SOME CONSIDERATIONS CONCERNING THE PRINCIPAL EQUATION FOR THE AERODYNAMIC CALCULATION OF NON-RADIAL CALCULATION STATION ON S2 STREAM-SURFACE FLOW IN TURBOMACHINES
    关于叶轮机械非径向计算站的S_2流面气动计算主方程的讨论
短句来源
    SOME BASIC PROBLEMS AND ENGINEERING APPLICATIONS OF BOUNDARY INTEGRAL EQUATION BOUNDARY ELEMENT METHODIN ELASTICITY
    边界积分方程—边界元法的基本理论及其在弹性力学方面的若干工程应用
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    THE LAGRANGIAN BOUNDARY LAYER EQUATION AND THE UNSTEADY SEPARATION OF THE ELLIPTIC CYLINDER AT ANGLE OF ATTACK
    拉格朗日边界层方程及椭圆柱在攻角下的非定常分离
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  公式
    In this paper the direct boundary integral equation deduced by Green’s formula and the fundamental solution is considered to solve Seepage problem. After the boundary is discrete, the numerical solution is gained by solving linear system of equations and by calculating the discrete integration expression of solution.
    本文利用Green公式和基本解推导得出直接边界积分方程来求解渗流问题,经边界元离散后,通过求解线性代数方程组和计算解的离散的积分表达式求得原问题的数值解,该方法需要在边界上计算积分,文中分别用解析积分法和高斯数值积分计算公式
短句来源
    The valueof the exponents n in the buffer zone is 2-3. In the turbulent region M = 1.0, n varies with Rex such that n = 1.17Rex0.135, and the logarithmic equation u +=5.95 log y+ + 5.48 can be used.
    紊流区中M=1.0,n值随Re_x而变化,n=1.17Re_x~(0.135)紊流区也可用对数公式u~+=5.95logy~++5.48。
短句来源
    The dynamic coefficients are calculated using the formula deduced from Navier-Stokes equation.
    动力系数根据由Navier-Stokes方程导出的公式计算。
短句来源
    3. an approximate equation of curvature correction factors F_c is proposed.
    3.拟合出了曲率修正因子F_c的近似计算公式.
短句来源
    A formula of the frequency change has been deduced from the wave equation to the first order approximation.
    从波动方程出发,导出频率改变的一级近似公式
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  方程组
    Singular Integral Equation Groups for 3-D Crack Problems in Finite Body
    有限体三维断裂的奇异积分方程组(英文)
短句来源
    The Basic Equation Group of Rheological Material Containing Defects (Ⅰ)
    含缺陷流变性材料的基本方程组(Ⅰ)——热-力耦合效应的实验研
短句来源
    On the Basic Equation Group of Rheological Material Containing Defects
    论含缺陷流变性材料的基本方程组(英文)
短句来源
    The Basic Equation Group of Rheological Material Containing Defects (Ⅱ)
    含缺陷流变性材料的基本方程组(Ⅱ)——热磁特性的实验研究
短句来源
    Canonical Systems and Symplectic Scheme for Four Order Rod Vibration Equation
    四阶杆振动方程的正则方程组及其辛格式
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  方程中
    On the Coupling Terms Between the Motion of Structure and Fluid in Morison Equation
    关于Morison方程中耦合项的研究
短句来源
    BEM Dual Reciprocity Method for N S Equation
    双重互易边界元法在求解 N-S 方程中的应用
短句来源
    Governing equations adopted are Stokes equation for momentum and Laplace equation for energy.
    由于研究对象是小液滴缓慢的热毛细迁移过程,因而所采用的控制方程中动量方程为StokeS方程、能量方程为Laplace方程。
    Traveling Wave Speed and Solution in Reaction- Diffusion Equation in One Dimension
    一维反应扩散方程中的行波波速及行波解
短句来源
    The Simplified Means About the Coefficient and Free Item of Displacement Method Equation
    位移法方程中系数与自由项的简化求法
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      equation
    For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation.
          
    The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type.
          
    The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered.
          
    As applications, the wave equation on?+ × ?+ and the heat equation in a semi-infinite rod are considered in detail.
          
    Pointwise fourier inversion: A wave equation approach
          
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    In dealing with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully examined. In the previous paper, we gave the resistance acting on a sphere moving in a non-uniform flow field. In this paper, we assume the concentration of sand particles to be very small, and using the previously obtained formula...

    In dealing with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully examined. In the previous paper, we gave the resistance acting on a sphere moving in a non-uniform flow field. In this paper, we assume the concentration of sand particles to be very small, and using the previously obtained formula for the resistance, we establish the general equations of motion of laminar flow of sand particles and water. Then, we discuss the sedimentation motion of sand particles for laminar flow in an open channel.Finally, we find that the component of relative velocity parallel to the main stream is not equal to zero. Thereby, we obtain the error in the position of sedimentation as calculated by means of the usual simplified assumption. This error in position is proportional to the depth of water, and is independent of the size of sand particles. In general, it is not a negligible quantity.

    在前文中我们已经给出小球在不均匀流场中运动时所受到的阻力。本文中我们假定泥沙和水为两种不同的介质,同时假定泥沙的浓度很小。利用前文所得到的阻力公式,我们建立了在层流状态时泥沙和水各自的运动方程组。然后利用这一组方程来讨论明渠中水流流态为层流时泥沙沉淀的情况。最后我们得到泥沙和水的相对速度在主流方向的分量并不等于零。同时我们求得根据简单假定来计算时所引起的沉积位置的误差。这个误差和水深成正比而和泥沙颗粒的大小无关。一般说来,这个误差并不是一个可以忽略的数值。

    Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear...

    Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear terms in the dynamical equations can be neglected. Furthermore the size of vortices which form the turblent flow is regarded small, so within the range of each vortex the mean turbulent velocity and its gradient can be considered to be independent of the changes of the space coordinates. We now seek the following approximate solution of the linearized equations of turbulent velocity fluctuation; one part of the turbulent velocity fluctuation represents the final stage motion of homogeneous isotropic turbulence, while the other is proportional to the gradient of mean velocity, the latter part being smaller than the former. From this approximate solution the shearing component of the Reynolds stress is found to be directly proportional to the gradient of mean velocity. As a special example of the general solution we consider the case of the two-dimensional wake. Within the wake we put, furthermore, a plane grid normal to the plane of symmetry of the wake. This grid then creates in its downward stream a homogeneous isotropic turbulence field superimposed upon that of the wake. Our solution is applicable to places far downstream both from the body which creates the wake and from the grid. Since the flow here is nearer to the grid, so the turbulence level of the homogeneous isotropic turbulence would be higher than that of the wake. Consequently the conditions of the general solution can be satisfied. The present paper presents the solutions of the mean velocity and the mean squares of turbulent velocity fluctuation of the wake. These theoretical results can all be tested by experiment. On account of that we only discuss the final stage motion of free turbulence, the question how to lay down the upstream boundary condition of the flow field when solving the differential equations of the mean flow needs further consideration by other methods.

    具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速...

    具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速和速度涨落平方平均值的解。?

    Because of the fact that there exists a mathematical identity between the statically indeterminate moments in the compatibility equation and the fiber stresses in the equation of eccentrically loaded columns, in analyzing singly-connected (single cell) rigid frames with degree of redundancy not more than 3, it is usually possible to use the familiar formula for short columns eccentrically loaded to analyse the indeterminate moments, which is called the column analogy. This method which is simple...

    Because of the fact that there exists a mathematical identity between the statically indeterminate moments in the compatibility equation and the fiber stresses in the equation of eccentrically loaded columns, in analyzing singly-connected (single cell) rigid frames with degree of redundancy not more than 3, it is usually possible to use the familiar formula for short columns eccentrically loaded to analyse the indeterminate moments, which is called the column analogy. This method which is simple and straight-forward, is becoming one of the convenient tools in structural analysis.For multi-connected (multi-cell) rigid frames which are composed of many singly-connected rigid frames and have degree of redundancy more than 3, the analysis becomes more difficult and the column analogy cannot be applied directly. Generally the moment-distribution method is used and the column analogy is only used for the determination of various constants such as fixed-end moments, stiffness factors and carry-over factors for use in the method of moment distribution.The present paper gives an extension of the column analogy, making it applicable to the analysis of multicell problems. Each cell is analogized by a single column. The influences of the common member of two neighbouring cells are studied and the results are represented by corrections in the load and moments carried by the column. Once the -corrected loading for each cell is determined, further computation is just the same as in the ordinary column analogy.

    在解析小於三次靜不定的單空剛構時,由於變形諧調條件中,靜不定彎矩的關係式與直柱偏心受壓中應力的關係式形式相似,常可利用在材料力學中已熟悉的偏心受壓柱公式來幫助解析,這就叫做柱比分析法。方法簡明,不易錯誤,為計算上很便利的方法之一。 由許多單空剛構組合起來的多空剛構的靜不定次數大於三,解析即比較繁雜,不能直接採用柱比法。通常可採用彎矩分配法,而僅用柱比法來求出各個桿件的各種常數,如傳遞係数、分配係數等,供分配法运算之用。 本文將柱比法予以推廣,使能應用到多空剛搆的解析。方法系将每一“空”看成一個柱,研究相鄰两“空”间共同桿件的影响,進而修正柱上所负担的荷重。求得每一個空的修正荷重後,计算即与一般的柱比法相同。

     
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