Papers by Keyword: Boundary Collocation Method

Abstract: Coal usually contains many cracks which affect the stability of mining zone. In order to research the fracture mechanism of cracked coal, a special case of three collinear cracks filling with gas is considered. A set of complex stress functions which satisfy all the required conditions are first derived, based on Muskelishvili’s results. The least square boundary collocation method is used to enforce the external boundaries approximately, and the stress intensity factors (SIF) can then be computed according to the related formulae. The value of SIFs for different crack orientations, different crack distance under different loading are calculated. The results shows that the most unfavorable crack orientation is in the 45° angle and the confining stress and the distance between cracks have a considerable effect on the SIF value.

Abstract: The existence of water affects the mechanical properties of cracked rock mass. Taking into account the friction generated by the crack closure, the stress intensity factor of the center cracked plate subjected to compression and seepage pressure was obtained through the theoretical analysis and numerical calculation of the boundary collocation method. The results show that crack tip stress intensity factor increases with the increasing of the seepage pressure, but decreases with the increasing of crack surface friction and the confining pressure. Finally a failure criterion for cracked rock mass under seepage pressure and confining pressure is developed.

Abstract: A two-dimensional electromechanical analysis is performed on a transversely isotropic piezoelectric material containing a crack based on the impermeable electric boundary condition. By introducing stress function, a general solution is provided in terms of triangle series. It is shown that the stress and electric displacement are all of 1/2 order singularity in front of the crack tip. In addition, the electromechanical fields in the vicinity of the crack when subjected to uniform tensile mechanical load are obtained using boundary collocation method.

Abstract: The problem of an interface edge crack between two dissimilar piezoelectric materials is analyzed under the conditions of anti-plane shear and in-plane electrical loading. The crack is considered to be traction-free, but electric permeable one across which the normal component of the electric displacement are continuous. A series form of electromechanical solution and field intensity factors are obtained. The results show that all fields including strain, stress, electric field strength and electric displacement are singular in the front of crack tip. At last, the stress intensity factor is solved by the boundary collocation method (BCM), numerical results are given and discussed.

Abstract: The problem involving a center crack in a rectangular piezoelectric body under anti-plane mechanical shear loading and plane electrical loading is analyzed for the permeable crack face conditions. The so-called general solutions of stress and electric fields are obtained, which is satisfied both the governing equations of anti-plane problems and the boundary conditions of the crack face. It is shown that electric field is nonsingular near right crack tip, while strain, stress and electric displacement have crack-tip singular behavior, the energy release rate has the same form as that without the electromechanical interaction, which is always positive. At last, the boundary collocation method is used to calculate the energy release rate. Numerical values are obtained to show the influence of the material properties and the electric field. The results show that the method of half analytical and half numeral is simple, accurate and widely applicable.