Liu Dian-kui

SCATTERING OF SH-WAVES BY AN INTERACTING INTERFACE LINEAR CRACK AND A CIRCULAR CAVITY NEAR BIMATERIAL INTERFACE

An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Greens function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Greens function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Greens function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different medial upon DSIF and DSCF.

Scattering of Plane SH-Wave by a Cylindrical Hill of Arbitrary Shape

The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Furthermore appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacement of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method (FEM).

The interaction of plane SH-waves and non-circular cavity surfaced with lining in anisotropic media

In this paper, we use the complex function method for solving the problem of interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media. Anisotropic media can be used to simulate the conditions of the geology. This problem can be handled by using the method similar to that incorporated in Ref. [5] to define the scattering waves in media, added with the given boundary condition of the circular cavity.In this paper, as illustrated in the examples, the results and discussions of numerical studies have been done for the interaction of plane SH-waves and two kinds of circular cavities, surfaced with lining made up of different materials, in anisotropic media.

Scattering of circular cavity in right-angle planar space to steady SH-wave

Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the mothod introduced here.

Scattering of SH-wave by cracks originating at an elliptic hole and dynamic stress intensity factor

The method of complex function and the method of Greens function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Greens function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN’S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping, scattering of flexural waves and dynamic stress concentrations in Mindlins thick plates with a cutout have been studied. The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique, the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations. As examples, numerical results for the dynamic stress concentration factor in Mindlins plates with a circular, elliptic cutout are graphically presented in sequence.

Scattering of plane SH-waves on cylindrical canyon of arbitrary shape in anisotropic media

The complex function method is used to solve problems of scattering of plane SH-waves on cylindrical canyon topography of arbitrary shape in anisotropic media. This paper gives the complete function series and general expressions with boundary condition to approach the solution of steady state scattering of plane SH-waves on two-dimensional canyon topography in anisotropic media. The problem to be solved can be reduced to a solution of infinite algebraic equation series by using Hermite function and its orthogonal conditions. The solution can be obtained directly by using computers. Finally, as an example, computational results of scattering of plane SH-waves on a semi-cylindrical canyon topography are presented.

Dynamic stress concentration around a circular hole due to SH-wave in anisotropic media

A new approach based on complex function to solve the SH-wave scattering problem around a circular hole in anisotropic media is introduced in this paper. It is found that the dynamic stress concentration factor is dependent on the incident wave number and the hole radius. Finally, some numerical results of dynamic stress concentration factor of a circular hole in anisotropic media are given.

A damage function used for prediction of low cyclic fatigue life

In this paper, the cyclic plastic strain energy is acted as damage variable and its mathematical model of transient response is established. The nonlinear fatigue damage function is given by means of the damage mechanical method. The formula used for prediction of low cyclic fatigue life is obtained from this damage function which takes into acount the cyclic relativity of cyclic plastic strain energy. The low cyclic fatigue life predicted by this formula is in correspondence with the experimental results.

Scattering of plane SH-waves on semi-canyon topography of arbitrary shape with linging in anisotropic media

The purpose of this paper is to use the conforma mapping method[1] to analyze and evaluate the ground displacement and scattering of incident SH-waves, on the surface of semi-canyon topography of arbitrary shape with lining in anisotropic media. The problem to be solved can be reduced to the solution of an infinite algebraic equation set by using the method of full-space expansion of Fourier progression. Using the mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitrary shape into a cylindrical canyon in full-space. Moreover, it is far practical in engineering practice. From the computational examples, it is obvious that the variation of displacement amplitudes on the surface near the lining and the canyon topography is rather sharp, especially when the freqencies of incident SH-waves increase.