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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.