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对偶积分方程     
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  dual integral equations
     By Hankel integral transform, the problem is reduced to a set of dual integral equations which are transformed into a set of singular integral equations.
     文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组.
短句来源
     The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined.
     通过应用Fourier分析和对偶积分方程理论 ,得到了立方准晶材料Ⅲ型裂纹问题的精确解析解 ,并由此确定了位移与应力场 ,应力强度因子和应变能释放率 .
短句来源
     A Class of Two-Dimensional Dual Integral Equations and Its Application
     一类二维对偶积分方程的解及其应用
短句来源
     by using the Fourier integral transform and the boundary conditions, the problem is reduced to a dual integral equations. The dynamic stress intensity factors at the crack tip are obtained by the using Copson methods and the numerical integral technique. As an example, the eects of the parameter and the frequency of SH wave on norm dynamic stress intensity factors are discussed.
     研究了正交各向异性功能梯度材料中直裂纹对SH波的散射问题,材料两个方向的剪切模量和密度假定为指数模型,通过积分变换-积分方程方法,建立数学模型,化为对偶积分方程,用Copson方法求解对偶积分方程,最后得到动应力强度因子,并且给出了数值算例,讨论了在SH波作用下,裂纹尖端的动应力强度因子与入射波的频率,入射角的关系.
短句来源
     In the present paper,the dual integral equations with complex exponential function are studied based on solving method of copson.
     在断裂力学和热弹性动力学中,常常会出现含复指数函数对偶积分方程的求解,此类方程不能直接用Copson-S ih方法求解。
短句来源
更多       
  dual integral equation
     In this paper,from the definition of Mellin transform we derive it's inversion theorem and solve a dual integral equation by using above result:
     本文从梅林变换的定义出发导出其反演定理及基本性质,并用此变换求解对偶积分方程
短句来源
     :This paper studies the propagation of crack problem in dynamic fracture mechanics, and obtains the analytical expressions of the stress and displacement fields and dynamic stress intensity factor by using Fourier analysis and theory of dual integral equation.
     本文研究了断裂动力学中的传播裂纹问题,运用Fourier分析与对偶积分方程理论,得到了应力场与位移场的精确解析表达式,以及表征动态断裂的特征参量-动态应力强度因子。
短句来源
     The mixed boundary value problem is reduced to a dual integral equation by means of nonlocal linear elasticity theory and integral transform method The stress field and displacement field for an infinite strip of FGM are solved near the tip of a crack by using Schmidt’s method.
     利用非局部线弹性理论和积分变换方法,将混合边界值问题简化对偶积分方程,最后通过Schmidt方法对裂纹尖端的应力场和位移场进行了求解。
短句来源
     The problem of the crack is reduced to a simultaneus system of dual integral equation by means of the method of integral transforms.
     本文用积分变换的方法将问题的解归结为求解一个对偶积分方程
短句来源
     The mixed boundary value problem is reduced to a dual integral equation by means of nonlocal linear elasticity theory and Fourier integral transform method. The stress field and displacement field for an infinite strip of FGM are solved near the tip of a crack by using Schmidt's method.
     利用非局部线弹性理论和Fourier积分变换方法,将混合边界值问题简化为对偶积分方程,最后通过Schmidt方法对裂纹尖端的应力场和位移场进行了求解。
短句来源
更多       
  a pair of dual integral equations
     By using the Fourier transform,the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces.
     通过Fourier变换,问题可以转换为对一对未知变量是裂纹表面位移差的对偶积分方程求解.
短句来源
     Fourier transforms are used to reduce the problem to a pair of dual integral equations, which are then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor is determined.
     应用Fourier积分变换将问题化为以第二类Fredholm积分方程表示的对偶积分方程,导出了相应的动应力强度因子表达式。
短句来源
     Based on the Biot’s dynamic equations, the vertical vibration of a rigid strip foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of Fourier integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary value condition and the continuity condition.
     根据Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上刚性条形基础竖向振动的对偶积分方程,并将其退化到完全饱和地基的情形。
短句来源
     Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition.
     运用作者提出的饱和土弹性波动方程 ,从理论上研究了上覆单相弹性土层的饱和地基上刚性基础的竖向振动轴对称问题 ,即采用Hankel积分变换技术并按混合边值条件建立了部分饱和地基上刚性基础竖向振动的对偶积分方程 ,并将其蜕化为完全饱和地基的情形 ;
短句来源
     At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.
     首先,采用Fourier积分变换解析求解了Biot方程,得到了该动力控制方程在Fourier变换域上的一组通解,然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程,并应用Jacobi正交多项式将其转化为一组线性代数方程组,通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv,编制了相应的计算程序。
短句来源
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  “对偶积分方程”译为未确定词的双语例句
     This study gives the computation of some typical dynamic stress intensity factors of mode I, II and III for two or three dimensional cracks under transient loading, making use of integral transforms and dual integral epuations.
     本文用积分变换与对偶积分方程的方法,计算了几类典型瞬态载荷作用下的二维与三维裂纹的Ⅰ、Ⅱ、Ⅲ型动态应力强度因子。
短句来源
     Using Abel anti-transformation,the equations can be reduced to regularized Fredholm integral equations of the second kind.
     文中基于Copson-S ih方法,证明了含余弦函数的对偶积分方程可化为第二类Fredholm积分方程进行数值求解。
短句来源
     By using the Copson method, one of these equations is transformed into a Fredholm integral equation of the second kind to obtain the solution. Furthermore, the intensity factors, the total energy release rate and the mechanical strain energy release rate are obtained and compared with the classical results without considering the electric field gradient effects.
     采用了Copson方法,将其中一组对偶积分方程转化为第二类Fredholm 积分方程来进行数值求解,得到了裂纹尖端的强度因子、总能量释放率和机械应变能释放率,并与经典理论中的结果进行了比较。
短句来源
     We get the displacement, stress, electric potential and electric displacement around the crack in an infinite plane of functionally graded piezoelectric materials, a half plane of functionally graded piezoelectric materials and a strip of functionally graded piezoelectric materials by Fourier Transforms, respectively.
     首先使用Fourier变换,然后求解对偶积分方程,分别给出了无限大、半无限大及带型压电体中应力、电势、电场强度及电位移的解析表达式;
短句来源
     The accuracy of the solution lies in the boundary collocation technique.
     把二维对偶积分方程化简成无限代数方程组,此方法的精确度取决于计算点的配置(即所谓边界配置).
短句来源
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  dual integral equations
By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces.
      
To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials.
      
Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces.
      
To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials.
      
This problem is reduced by means of Fourier transforms to the standard set of dual integral equations with two variables.
      
更多          
  dual integral equation
Thus, the analytical solution for the temperature with respect to the spatial variables reduces to a dual integral equation.
      
The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih.
      
The results of this paper are very close to those given by the two-dimensional dual integral equation method.
      
The present problem can be solved by using the Fourier transform and the technique of dual integral equation, in which the unknown variable is the jump of displacement across the crack surfaces, not the dislocation density function.
      
A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem.
      
更多          
  dual_integral equation
Thus, the analytical solution for the temperature with respect to the spatial variables reduces to a dual integral equation.
      
The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih.
      
The results of this paper are very close to those given by the two-dimensional dual integral equation method.
      
The present problem can be solved by using the Fourier transform and the technique of dual integral equation, in which the unknown variable is the jump of displacement across the crack surfaces, not the dislocation density function.
      
A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem.
      
更多          
  a pair of dual integral equations
By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces.
      
The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition.
      
By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable was the jump of the displacements across the crack surfaces.
      
Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem.
      
By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces.
      
更多          


In this paper, the three-dimensional elastic solid with internal rectangular crack is considered. Let the crack surfaces be subjected to equal and opposite normal tractions p0. This problem is reduced, by means of Fourier transforms, to the standard set of dual integral equations with two variables. Then the fomulas of analytic solution of the displacements on the crack surfaces and of the stress-intensity factors of crack border are obtained.

本文分析了含有矩形片状裂纹(裂纹上下表面受均匀压力作用)的三维弹性体.借助Fourier积分变换.将问题化归为二个变数的对偶积分方程,并获得裂纹面位移和裂纹前缘应力强度因子的解析表达式.

A new method for calculation of stresses strains and displacements in an

本文提出了一种计算刚体压缩课题的新方法,这就是将原来的混合边值问题变换为等价的应力边值问题,从而避开了求解对偶积分方程的困难,使本课题得到了比较圆满的解决。

In this paper, the problem of the plane circular crack in a homogenous and isotropic infinte elastic body under circumferential load at infinity parallel to the plane of the crack is studied within the linearized couple-stress theory by Mindlin and Tiersten. The problem of the crack is reduced to a simultaneus system of dual integral equation by means of the method of integral transforms.This system, in turn,is reduced to a one-dimensional integral equation of Fredholm's second kind that is amenable to a numerical...

In this paper, the problem of the plane circular crack in a homogenous and isotropic infinte elastic body under circumferential load at infinity parallel to the plane of the crack is studied within the linearized couple-stress theory by Mindlin and Tiersten. The problem of the crack is reduced to a simultaneus system of dual integral equation by means of the method of integral transforms.This system, in turn,is reduced to a one-dimensional integral equation of Fredholm's second kind that is amenable to a numerical treatment. Stress singularities around the edge of the crack are considered, and the stress intensity factor is calculated. The results obtained show that the order of the stress sigularities is the same as that of the classical stress singularities, but owing to the effect of the couple-stress, the magnitude of the stress factor is lower than the classical theory's and changes with parameters of the material, 1 and η.

本文根据Mindlin&Tiersten的线性偶应力理论研究了含有圆盘状裂纹的无限大体,在无限远处、平行于裂纹的周向剪应力的作用下,应力在裂纹尖端处的奇异性。本文用积分变换的方法将问题的解归结为求解一个对偶积分方程。最后通过解析结合数值分析求得对称应力在裂纹尖端处的应力强度因子。结果表明:由于偶应力的影响,裂纹附近应力集中的程度较之经典弹性理论的结果有所下降,并且与新增加的弹性常数l和η有关。

 
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