A boundary value method for the singular behavior of bimaterial systems under inplane loading

Based on the governing equations of linear elasticity, this paper develops a novel boundary value method to study the singular behavior of elastic stress fields at the corners of bimaterial wedges and junctions by using the eigenfunction expansion technique. The resulted one-dimensional differential system, which consists of the reduced equilibrium equations and boundary conditions, just relates to an angular coordinate in the polar coordinate system. Implementing discretization of this differential system by the finite cloud method, we readily derive the so-called generalized eigenproblem in the singular eigenvalue. The performance of the methodology is subsequently verified through the well-known crack and interface crack problems, demonstrating high accuracy and quick convergence characteristics. In addition, a selected set of practically useful models is numerically analyzed to examine the angular variations of the displacement and stress fields, and the influences of wedge-side boundary conditions to singular behavior are also studied.