Dynamic element discretization method for solving 2D traction boundary integral equations

A sufficient condition for the existence of element singular integral of the traction boundary integral equation for elastic problems requires that the tangential derivatives of the boundary displacements are Hِlder continuous at collocation points. This condition is violated if a collocation point is at the junction between two standard conforming boundary elements even if the field variables themselves are Hِlder continuous there. Various methods are proposed to overcome this difficulty. Some of them are rather complicated and others are too different from the conventional boundary element method. A dynamic element discretization method to overcome this difficulty is proposed in this work. This method is novel and very simple: the form of the standard traction boundary integral equation remains the same; the standard conforming isoparametric elements are still used and all collocation points are located in the interior of elements where the continuity requirements are satisfied. For boundary elements with boundary points where the field variables themselves are singular, such as crack tips, corners and other boundary points where the stress tensors are not unique, a general procedure to construct special elements has been developed in this paper. Highly accurate numerical results for various typical examples have been obtained.