A Displacement Discontinuity Method of High-Order Accuracy in Fracture Mechanics

In this paper the displacement discontinuity method of high-order accuracy and its application to the problems of fracture mechanics are considered. In common practice of applications of boundary element methods, the methods with the piecewise-constant function of boundary displacement are often used. Their advantage against other algorithms is the simplicity of calculation scheme with a rather good accuracy of the solution at the points of region distant from the boundary. In the fracture mechanics (with lines of surfaces of discontinuity of the displacement field), it is required to describe the stress behavior in the proximity of the crack edges with the highest accuracy possible, which leads to necessity of increasing the degree of accuracy of the used numerical methods. It is shown that the methods with high-order continuity of displacements at the boundary proposed in this work substantially improve the accuracy of computation of displacement and stress fields in the neighborhood of crack edges within the region.