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.

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.

Fourier transform is employed to reduce to this mixed boundary value problem to three pairs of dual integral equations; also the new additional boundary conditions are discussed.

By integral transform method, the scattering of elastic wave by two cracks is reduced to a set of dual integral equations which are further transformed to a set of singular integral equations of the first kind. By means of Chebyshev polynomials of the first kind, the solutions of the singular integral equations have been obtained, and the formulae of the dynamic stress intensity factors are presented.

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.

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.

In the present paper the general representations for the solution of the dynamical crack problems of the laminated media consist of different orthotropic layer are derived. Using conditions of the welding surfa.ce, we express all the quantities in terms of a single unknown function. Using method of integral transform, we formulate the impact loading problem as dual integral equations. Using the Copsons method, the solution is derived. The method in the paper is not difficult to generalize for the case of an...

In the present paper the general representations for the solution of the dynamical crack problems of the laminated media consist of different orthotropic layer are derived. Using conditions of the welding surfa.ce, we express all the quantities in terms of a single unknown function. Using method of integral transform, we formulate the impact loading problem as dual integral equations. Using the Copsons method, the solution is derived. The method in the paper is not difficult to generalize for the case of an arbiritrary loading applied to the crack.