Two-dimensional direct boundary integral method for multilayered elastic media

This paper concerns the development of a 2-D direct boundary integral method for elastostatics boundary value problems in multilayered media. The method is based on the analytical solution to the problem of a concentrated force within 3ne of two bonded half-planes in which the interface continuity conditions are fulfilled exactly. A four-layer elastic region is developed by using a substructing approach to construct a "numerical interface" between two different bonded half-plane regions. Higher order (linear) boundary elements are used to model all boundary contours and the numerical interface. The model uses straight line elements, and all integrations are done analytically. Zero-length elements are used at corners, or at points where the prescribed loading is discontinuous. Infinite elements are used at the extremities of the numerical interface to reduce numerical errors due to truncation. Three sets of example problems are used to verify the model described in this paper: (1) a circular hole in an infinite strip loaded in tension at infinity; (2) a circular hole near the surface of a half-plane; and (3) a circular cavity within one of two bonded half-planes. The numerical results obtained are in good agreement with the published solutions for these problems. In order to demonstrate the efficacy of the method, the numerical results for the problem of a circular cavity in a four-layer infinite region are also presented in this paper.