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second kind
相关语句
  第二类
    THE SECOND KIND BOUNDARY INTEGRAL EQUATIONS IN THREE DIMENSIONAL FRACTURE MECHANICS
    三维裂纹问题的第二类边界积分方程
短句来源
    THE FUNDAMENTAL SOLUTIONS FOR THE SECOND KIND BOUNDARY INTEGRAL EQUATION——BOUNDARY ELEMENT METHOD OF THE PLANE AND ANTIPLANE PROBLEMS
    平面问题及反平面问题的第二类边界积分方程——边界元方法的基本解
短句来源
    The Unified Second Kind Boundary Integral Equation in Fracture Mechanics
    断裂力学中统一的第二类边界积分方程
短句来源
    GENERALIZED LAGRANGE'S EQUATION OF THE SECOND KIND AND ITS APPLICATION IN NONHOLONOMIC SYSTEMS OF ANALYTICAL DYNAMICS
    广义第二类拉格朗日方程及其对非完整力学系统的应用
短句来源
    Discussion of the Application of Lagrange's Equation of the Second Kind
    对拉格朗日第二类方程的应用探讨
短句来源
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  二类
    But in the case of interface cracks, the problem leads to solve a pair of Cauchy-type singular integral equations of the second kind, which differs basically in coefficients of the equations obtained from the interface crack problems of bonded isotropic strips.
    但在界面裂纹时,却归结为解一组与各向同性粘接板条不同的二类柯西型奇异积分方程.
短句来源
    Finally, degenerating the present results, the expressions of the second foundamental solution and the second kind boundary integral equation in the related literature are given.
    最后,经过退化处理给出了目前有关文献中发表的第二基本解及第二类边界积分方程的各种具体表式。
短句来源
  “second kind”译为未确定词的双语例句
    An effective finite element method is developed for the second kind of finite deformation constitutive relation scheme and is used to study the plane strain, mode I static crack tip field. Once more, it is established that TNT plasticity can predict a significant stress increase in the vicinity of crack tip. Compared with that in infinitesimal TNT plasticity, the crack tip stress singularity in finite deformation TNT plasticity is closer to the square-root singularity of classical elastic K field.
    为后面的一种大变形本构方案发展了一套有效的有限元方法:并应用于平面应变Ⅰ型静止裂纹尖端场的研究,再一次证实了TNT非局部理论可以明显地提高裂纹尖端附近的应力水平,大变形预测的裂尖应力场的奇异性更接近于经典弹性K场的平方根奇异性。
短句来源
    Kolosov-Muskhelishvili complex potentials are constructed as integral representations. As a result, the considered problem is reduced to a system of singular integral equations of the first and the second kind.
    给出了积分形式的Kolosov-Muskhelishvili复势,并进一步将所考虑问题转化为第一型或第二型的奇异积分方程组。
短句来源
    A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composits is presented in the peper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer are dedued from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained by using the iteration solution of Fredholm integral equation of second kind.
    本文对纤维增强复合材料桥联增韧进行了详细的断裂力学分析.基于Castigliano's定理和界面剪滞(Shear-lag)模型,得到了含界面相效应的复合材料桥联增韧和裂纹张开位移的控制方程;
短句来源
    Making the transformation of an unknown function, the bending problems of rectangular plates of unidirectionally varying stiffness with two opposite edges simply supported under any normal load distribution are reduced to solving the Volterra integral equations of the second kind.
    本文通过做未知函数变换,将两对边简支单向变刚度矩形板在任意横向分布载荷作用下的弯曲问题归结为求解第二类的Volterra积分方程。
短句来源
    In the field of theoretical geophysical fluid dynamics, the contents are: long-wave dynamics and linear stability problems, weakly-nonlinear theory and planetary-wave dynam-ics, nonlinear stability criteria of atmospheric and oceanic motions established by Arnold method (ener-gy-Casimir method), the evolution of disturbance, the interaction of disturbance and basie state, and the conditional instability of the second kind (CISK) in the tropical atmospheric dynamics.
    在理论地球流体力学方面,介绍了长波动力学及线性稳定性问题、弱非线性理论及行星波动力学以及用Arnold方法(能量-Casimir方法)研究大气和海洋中各种流体运动的非线性稳定性问题的成果。
短句来源
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  second kind
An FEM approximation for a fourth-order variational inequality of second kind
      
A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered.
      
The elements of this set are represented by the systems obeying the Lagrange equations of the second kind and having also bounded inertial characteristics and generalized forces.
      
Peculiarities of electroosmosis of the second kind at the surfaces of one and two ionite granules
      
Electroosmosis of the second kind at the surfaces of one and two granules of a cationite and an anionite are studied by experimental methods.
      
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In this paper, the transient response of a pair of radial cracks which are of equal length and notched symmetrically from a borehole, hole-line-shaped (HLS) crack, is discussed in case of normal tractions being suddenly applied to the wall pf the borehole and the surface of the crack, which comes from the approximatioe of the initiation of the HLS crack under dynamic loading, that is, the first phasn of fracture control.Due to the complexity of the boundary and the existance of the inertia term in the dynamic...

In this paper, the transient response of a pair of radial cracks which are of equal length and notched symmetrically from a borehole, hole-line-shaped (HLS) crack, is discussed in case of normal tractions being suddenly applied to the wall pf the borehole and the surface of the crack, which comes from the approximatioe of the initiation of the HLS crack under dynamic loading, that is, the first phasn of fracture control.Due to the complexity of the boundary and the existance of the inertia term in the dynamic equation, neither the integral transform for space veriable nor the conformal mapping can be applied to this kind of problems directly. But from Tweed's work for a crack notched from a circular hole in static case, we can get some inspiration. The problem can be solved by decomposition-superimposition-iteration (DSI)method in the following steps. First the initial-boundary value problem is changed into the boundary value problem by means of Laplace transformation. Next the solution region is decomposed into two simple regions, one is a circular hole, the other is a finite Line-shaped crack.The solutions of the decomposed problems can be obtained by using the separation of variables and the Fourier transform respectively. The displacement and the slress components are derived upon the super-imposition of the solutions. They have satisfied some conditions naturally. Then inserting them into the other conditions, the dual integral equations are obtained,where V(r, p) is a series. The coefficients in it can be determined from the borehole boundary conditions.The unknown function D(aaaaaaaaaaaaaaaaa, p) is included in these coefficients. To solve (1),V(r, p)is regarded as the free term temporarily, the predictor corrector method has been applied here- predicting V(r, p) in ( 1 ) to solve D(α, p), then making use of the borehole conditions to correct V(r, p), the corrected V(r, p) is inserted into ( 1 ) to solve D(α, p) again until the mstable V(t, p) is obtained. Thus ( 1 ) can be reduced to the standard Fredhol integral equation of the second kind.when the radius of the borehole approximates to zero, the equation is identical with Sih's solution for relevant problem of finite line-shaped crack in 1972. The solution of the equation ( 2 ) is got by iteration mentioned above and it leads to the Laplace transforms of the stress components, subsequently they are inverted by a combination of numerical means and an application of the Cagniard-DeHoop inversion technique. It has shown that the space distribution of the singular stress field of the crack discussed here is the same as Sih obtained, while the dynamic stress intensity factor k1,(t) reflects the affecting of the borehole. These are essential information in the application of the current theory of fracture mechnics, The numerical calculations demonstrate the feasibility of the DS1 method and the results provide the quantitative basis for us to simplify the practical problem, and make us fully understand the interaction of wave and the crack in this problem. The inferences from above results are in agreement .with others' experiments. Upon this the reasonable loading method is recommended. Moreover a number of theoretic extensions of the work and the ways to carry out the technique (fracture control) simply and economically in practice are proposed. Among these the most important one is that the DSI method can be extended to study the problem of the HLS crack moving at a constant velocity, which comes from the approximation of the propagation of the HLS crack under dynamic loading.

本文讨论由钻孔壁刻出的两个对称径向裂纹在孔壁及裂纹面上突加正压力作用下的瞬态响应,此问题来自于控制断裂。借助于叠加原理和积分交换方法,问题简化对偶积分方程,基于预测校正法的概念将孔壁边界条件对此方程的影响解耦,从而得到了第二类Fredholm积分方程,以迭代法和Cagniard-DeHoop反演技术求得解。结果表明在此裂端奇异场的空间分布与Sih 1972年就相应线状裂纹问题所得相同,而动态应力强度因子k_1(t)反映了孔的影响,当钻孔半径趋于零时解趋于Sih的解;并使得我们对本问题中波和裂纹的相互作用有了全面的了解,基于此提出了较为合理的加载方法,此外还提出了对本文工作的一系列理论推广以及简便和经济地应用控制断裂技术的方法。

Static crack problems for symmetrical bonded orthotropic strips of finitewidth sandwich typa have been studied in this paper. In both cases of the center strip having internal crack and being completely broken, the methods of solutions and the results of stre(?)ingularity analyses are similar to the same cracked geometries of bonded isotropie strips. But in the case of interface cracks, the problem leads to solve a pair of Cauchy-type singular integral equations of the second kind, which differs basically...

Static crack problems for symmetrical bonded orthotropic strips of finitewidth sandwich typa have been studied in this paper. In both cases of the center strip having internal crack and being completely broken, the methods of solutions and the results of stre(?)ingularity analyses are similar to the same cracked geometries of bonded isotropie strips. But in the case of interface cracks, the problem leads to solve a pair of Cauchy-type singular integral equations of the second kind, which differs basically in coefficients of the equations obtained from the interface crack problems of bonded isotropic strips. It is found that the previous defini ion of stress intensity factors at tips of interface crack in bonded iso(?)opic strips is no longer valid in this case. After carefully examining these coefficients and then analyzing stress singular behaviour at the crack tip, a generalized definition of stress intensity factors for the interface crack in either bonded orthotropic strips or bonded isotropic strips is presented. Finally numerical results of above three cracked geometries are given, and the influen(?) of crack size, strip width and elastic constants on stress intensity factors are obtained.

本文研究了有限宽、粘接的对称SANDW(?)CH型正交各向异性板条的静裂纹问题.在中间板条有内部裂纹和完全断裂的两种情形,解法和应力奇异性分析的过程都和板条为各向同性时相似;但在界面裂纹时,却归结为解一组与各向同性粘接板条不同的二类柯西型奇异积分方程.此时,各向同性粘接板条界面裂纹的应力强度因子的定义已不再适用.本文提出一种广义的应力强度因子定义,并给出上述三种裂纹问题的算例,计算裂纹长度、板条宽度或弹性常数对应力强度因子的影响.

In this article the strength analysis of cracked plates repaired with composite patches is investigated. Emphasis is laid on the consideration of various viscoelastic behaviors of patches or adhesives. By taking the forces in the repaired zone as basic unknowns, the problem is formulated exactly and the stress intensity factors at crack tips are obtained in closed form for point bond cases. For full and partial bond cases, the problem is reduced to a Fredholm integral equat on of the first or second kind,...

In this article the strength analysis of cracked plates repaired with composite patches is investigated. Emphasis is laid on the consideration of various viscoelastic behaviors of patches or adhesives. By taking the forces in the repaired zone as basic unknowns, the problem is formulated exactly and the stress intensity factors at crack tips are obtained in closed form for point bond cases. For full and partial bond cases, the problem is reduced to a Fredholm integral equat on of the first or second kind, depending on whether the effect of the adhesives is excluded or included in the consideration. Through numerical solution of the Fredholm integral equations, the variation of the stress intensity factors with respect to time is obtained and presented in graphical and tabular forms for various patch sizes, viscoelastic models, locations of the patches and bonded ranges. The results indicate that the stress intensity factors increase progressively with time, or, the reinforcement effect of patches on cracked plates decays monotonously due to the viscoelastic behavior of patches or adhesives. This paper shows that the viscoelastic effect should be taken into account in the strength analysis of cracked structures repaired by composite patches and provides the idealized models, basic equations and solution methods for the problem.

本文研究用复合材料贴片修补含裂纹弹性板件的强度分析问题,着重考虑贴片或胶粘剂的各种粘弹性性质。获得了裂纹尖端应力强度因子及其随时间的变化关系,论述了复合材料贴片修补技术对结构强度的影响与作用。

 
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