Solutions of the interior and exterior boundary value problems in plane elasticity by using dislocation distribution layer

Based on a previous publication (Savruk, 1981), a dislocation distribution layer method for the solution of interior and exterior boundary value problem (BVP) is studied in more detail. Properties of an integral operator in the resulting integral equation are studied. It is proved theoretically that the tractions applied on the outer boundary should be in equilibrium. In addition, a dislocation distribution layer method for the solution of exterior BVP is also suggested. In the exterior BVP, the tractions applied on the boundary may not be in equilibrium. In the exterior BVP, one must consider the single-valued condition of displacements. The formulation in the exterior BVP is not same as in the interior BVP. In the process of discretization, a technique for balance of the numbers of resulting algebraic equations and unknowns is suggested. Numerical examples prove that the suggested method can give sufficient accurate results.