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transform equation
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  变换方程
     Transform equation and its nonlinearity were analyzed,and the bend function of sensitive element was given.
     给出了敏感元件的实际弯曲函数 ,分析了其变换方程及非线性。
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  “transform equation”译为未确定词的双语例句
     In this paper the law "Double amplitude A of Coda maximum ground motion is attenuated with the duration time t calculated from P-wave first motion "is inferred based on a great number of seismic data in Northeast China region:Gz=2.211gtz+lgAz (1)GH =2.261gtH +lgAH (2)And the Coda magnitude Mc formula in Northeast China region and the transform equation between Mc and Ms are established.
     本文用东北地区的大量地震资料导出了地震尾波最大地动双振幅A随P波初动起算持续时间t的衰减规律: G_Z=2.21lgt_Z+lgA_Z (1) G_H=2.26lgt_H+lgA_H (2) 由此建立了中国东北地区尾波震级M_C公式以及与M_S的换算关系。
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     (2) For the measurement of single tree volume, we provide a direct linear transform equation of two-dimensional image, instead of three-dimensional analytic work so that the process is simplified and the computational work is remarkably reduced.
     (2) 针对测定单株立木材积,提出了适合于单株立木测量的二维直接线性变换法的构像方程,而不作三维的解析处理,简化了操作过程,大量地减少了计算工作量;
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     I use the hyperbolic heat conduction and mass transform equation to solve the heat conduction problem with complicated boundary conditions and coupled heat and mass transfer problem by FDM numerically.
     利用修正后的双曲型热传导方程和质量传递方程对具有复杂边界条件的导热问题以及热、质耦合传递问题用有限差分的方法进行了数值求解。
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     The transform equation between the physical system and calculation system was deduced, which was discretized using the central difference method.
     推导了物理平面与计算平面之间的坐标转换方程,使用中心差分法对转换方程进行离散。
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     Based on the facts of the compression modulus E~+ not being equal to tension modulus E~- and the stress path followed in the soil around the pressuremeter prober being different from that in other tests, a transform equation between E_m and E_o is deduced. The equation is available in accordance with the test data of the loess in the northwest of China.
     本文考虑土受压缩时的模量E~+不同于其拉伸模量E~-和旁压探头周围土体遵循应力途径的特点,导出旁压模量和变形模量的关系式,并以我国西北黄土为例,证实这关系式的可行性。
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  相似匹配句对
     equation
     方程(之14)
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     ON THE EQUATION
     关于方程ф(x)=ф(y)
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     Differential equation and continuous wavelet transform
     微分方程和连续小波变换
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     Function Transform and the Solution to Schrodinger Equation
     函数变换与薛定谔方程求解
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     The E-Transform and Its Applications
     E变换及其应用
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  transform equation
Analyzing the apparent conductivity data obtained by the electromagnetic induction technique and drill-hole measurements at same location allows the construction of a transform equation for the apparent conductivity and sea ice thickness.
      
Wilson and Cowan subsequently used a method of time-coarse graining to transform equation 1.3 into the differential equation 1.2.
      
This restriction ensures that the summation in the DWT transform equation is finite.
      
Inversion theorem and residue theorem used to solve Laplace transform equation.
      


In this paper we, using the viscoelastic, correspondence principle. consider the energy fracture criteria for a variety of linear viscoelastic solids. This principle arises because of the similarity which exists between the governing viscoelastic equations after Laplace transforms with respect to time and the corresponding untransformed elastic equations. We may therefore use this correspondence to write down immediately the Laplace transforms of the associated viscoelastic expressions....

In this paper we, using the viscoelastic, correspondence principle. consider the energy fracture criteria for a variety of linear viscoelastic solids. This principle arises because of the similarity which exists between the governing viscoelastic equations after Laplace transforms with respect to time and the corresponding untransformed elastic equations. We may therefore use this correspondence to write down immediately the Laplace transforms of the associated viscoelastic expressions. By inverting these transformed equations, we may thus finally obtain formulae describing the energy fracture criteria of Maxwell, standard linear and Burgers solids, respectively.The analysis of this paper investigates the application of the energy balance fracture criteria to linear viscoelastic bodies. It is shown that:(a) The energy release rates of viscoelastic cracked bodies may be divided into two parts. One describes the effect of retarded elasticity, another part describes the effect of viscous flow;(b) Burgers solids, as well as Maxwell solids, exists a critical state. Because of the viscous flow, this state will arrive sooner or late:(c) The crack wilt propagate with high speed as soon as critical state of cracked bodies arrives;(d) In contrast to Maxwell and Burgers bodies, for standard linear cracked bodies, there exist a value of the load below which the critical state will never occur, exceed which then they will attain to the critical state sooner on later.

在本文,我们应用粘弹对应性原理探讨了各种线粘性固体的能量断裂判据。这项原理由于在对时间的Laplace变换后的基本粘弹性方程与相应的未经变换的弹性方程间存在相似性而成立,所以我们可利用这一对应性直接写出相关的粘弹性表示式的Laplace变换。于是,反演这些变换了的方程,我们最终分别得到表述Maxwell固体、标准线性固体和Burgers固体的能量断裂判据公式。本文的分析探讨了能量平衡断裂判据对线粘弹体的应用。它表明: (α) 粘弹性裂纹的能量释放率可分成两部分,一部分反映了延迟弹性效应,另一部分反映了粘性流效应; (b) 和Maxwell固体一样,Burgers固体也存在临界状态。由于粘性流的缘故,这一临界状态迟早要到来; (c) 裂纹体一旦到达临界状态,裂纹就将以高速扩展; (d) 与Maxwell物体和Burgers物体相反,标准线性裂纹体存在这样的一个载荷值,低于它时,永不会产生临界状态;高于它时,迟早会陷于临界状态。

A new transformation and method of solution of the laminar boundary layer equations is presented in this paper. From the transformed equations we see that the properties of a specific boundary layer can be determined by a so-called 'principal function' which appears as a parametric functional coefficient in the new equations. It can be proved that the velocity profile and other properties such as the shear stress factor at a specific section of the boundary layer are determined by the local...

A new transformation and method of solution of the laminar boundary layer equations is presented in this paper. From the transformed equations we see that the properties of a specific boundary layer can be determined by a so-called 'principal function' which appears as a parametric functional coefficient in the new equations. It can be proved that the velocity profile and other properties such as the shear stress factor at a specific section of the boundary layer are determined by the local value of the principal function in addition to the new longitudinal coordinate. On this basis, a simple method of solution of admissible accuracy is presented, which makes the otherwise tedious calculation of shear stress a very simple task.

本文对一般定常平面不可压缩层流边界层方程式提出了一种新的变换,从而使其变为一种新的形式。从所得方程式可以看出:任一边界层,其区别于其它边界层的特点,决定于出现在方程式中的“主函数”,还可证明:边界层某一截面处的速度剖面和摩擦应力因子等特性,决定于两个当地参数。本文据此提出了一个求定摩擦应力的简便方法,将摩擦应力的求定归结为“主曲线”的绘制,许多实例说明了所述方法的准确性、通用性和简便性。

There are some common difficulties encountered in elastic-plastic impact codes such as EPIC[1][2], NONSAP[3], etc. Most of these codes use the simple linear functions usually taken from static problems to represent the displacement components. In such finite element formulation, the strain and stress components are constants in every element. In the equations of motion, the stress components in general appear in the form of their space derivatives. Thus, if we use such form functions to represent the displacement...

There are some common difficulties encountered in elastic-plastic impact codes such as EPIC[1][2], NONSAP[3], etc. Most of these codes use the simple linear functions usually taken from static problems to represent the displacement components. In such finite element formulation, the strain and stress components are constants in every element. In the equations of motion, the stress components in general appear in the form of their space derivatives. Thus, if we use such form functions to represent the displacement components, the effect of internal stresses to the equations of motion vanishes identically. The usual practice to overcome such difficulties is to establish a self-equilibrium system of internal forces acting on various nodal points by means of transforming equations of motion into varia-tional form of energy relation through the application of virtual displacement principle. The nodal acceleration is then calculated from the total forces acting on this node from all the neighbouring elements. The transformation of virtual displacement principle into the varia-tional energy form is performed on the bases of continuity conditions of stress and displacement throughout the integrated space. That is to say, on the interface boundary of finite element, the assumed displacement and stress functions should be conformed. However, it is easily seen that, for linear form function of finite element calculation, the displacement continues everywhere, but not the stress components. Thus, the convergence of such kind of finite element computation is open to question. This kind of treatment has never been justified even in approximation sense. Furthermore, the calculation of acceleration of nodal points needs a rule to calculate the mass matrix. There are two ways to establish mass matrix, namely, lumped mass method and consistent mass method.141 The consistent mass matrix can be obtained naturally through finite element formulation, which is consistent to the assumed form functions. However, the resulting consistent mass matrix is not in diago-nalized form, which is inconvenient for numerical computation. For most codes, the lumped mass matrix is used, and in this case, the element mass is distributed in certain assumed proportions to all the nodal points of this element. The lumped mass matrix is diagonalized with the diagonal terms composed of the nodal masses. However, the lumped mass assumption has never been justified. All these difficulties are originated from the simple linear form functions usually used in static problems.

在EPIC、NONSAP等弹塑性撞击计算的有限元程序中,都有一些共同的弱点.所有这些程序,都采用静力学问题中常用的简单线性形状函数来描写各位移分量.在这样的有限元法中,应变和应力分量在每一有限元中都是常量.但在运动方程中,应力分量都是以它们的空间导数的形式出现的.于是,在采用了线性形状函数来表达的位移分量以后,应力分量对运动方程的贡献必恒等于零.克服这种困难的一般方法是通过虚位移原理,把运动方程化为能量关系的变分形式,从而建立既作用在结点上而又在每一有限元内自相平衡的人为内力平衡系统.把施加在某一结点上的所有相邻有限元的人为内力的作用叠加在一起,就能计算这一结点的加速度.但是从虚位移原理化为能量关系的变分形式时,要求位移和应力在积分域内处处连续.也就是说,要求位移和应力有限元都是协调的.我们很易看到,线性形状函数所描述的位移有限元是连续协调的,但其有关的应力分量在有限元界面上,则并不连续.所以,这样的有限元处理,是否收敛并无把握,即使从近似角度看,也是难以令人满意的.而且,为了计算结点的加速度,我们还应该有建立质量矩阵的计算规则.目前有两种计算方法:一种是集总(lumped)质量法,另一种是一致(consis...

在EPIC、NONSAP等弹塑性撞击计算的有限元程序中,都有一些共同的弱点.所有这些程序,都采用静力学问题中常用的简单线性形状函数来描写各位移分量.在这样的有限元法中,应变和应力分量在每一有限元中都是常量.但在运动方程中,应力分量都是以它们的空间导数的形式出现的.于是,在采用了线性形状函数来表达的位移分量以后,应力分量对运动方程的贡献必恒等于零.克服这种困难的一般方法是通过虚位移原理,把运动方程化为能量关系的变分形式,从而建立既作用在结点上而又在每一有限元内自相平衡的人为内力平衡系统.把施加在某一结点上的所有相邻有限元的人为内力的作用叠加在一起,就能计算这一结点的加速度.但是从虚位移原理化为能量关系的变分形式时,要求位移和应力在积分域内处处连续.也就是说,要求位移和应力有限元都是协调的.我们很易看到,线性形状函数所描述的位移有限元是连续协调的,但其有关的应力分量在有限元界面上,则并不连续.所以,这样的有限元处理,是否收敛并无把握,即使从近似角度看,也是难以令人满意的.而且,为了计算结点的加速度,我们还应该有建立质量矩阵的计算规则.目前有两种计算方法:一种是集总(lumped)质量法,另一种是一致(consistent)质量法.一致质量矩阵是通过正规的有限元计算求得的,它和?

 
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