Boundary integral equations for 2D elasticity and its application in discrete dislocation dynamics simulation in finite body: 1. General theory

A unified approach, originating from Cauchy integral theorem, is presented to derive boundary integral equations for two dimensional elasticity problems. Several sets of boundary integral equations are derived and their relations are revealed. Explicit expressions for materials with different symmetry planes are listed. Special attention is given to the formulation that is based on the tractions and the tangential derivatives of displacements along solid boundary, since its integral kernels have the weakest singularities. The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary, without involving the linear superposition technique that was often used in the literature. Its application in simulating discrete dislocation motion in a finite solid body is discussed.