A new boundary integral equation formulation is presented for two-dimensional linear elasticity problems for isotropic as well as anisotropic solids. The formulation is based on distributions of line forces and dislocations over a simply connected or multiply connected closed contour in an infinite body. Two types of boundary integral equations are derived. Both types of equations contain boundary tangential displacement gradients and tractions as unknowns. A general expression for the tangential stresses along the boundary in terms of the boundary tangential displacement gradients and tractions is given. The formulation is applied to obtain analytic solutions for half-plane problems. The formulation is also applied numerically to a test problem to demonstrate the accuracy of the formulation.

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