A new kernel in BIE and the exterior boundary value problem in plane elasticity

A new kernel with formulation of the relevant BIE (boundary integral equation) in plane elasticity is introduced. The new kernel is derived from a fundamental solution expressed in a pure deformable form. If the kernel is used, the regularity condition is satisfied for any loadings on the contour of the hole. The exterior boundary value problem is studied. The applied loadings on the contour in the exterior boundary value problem may not be in equilibrium. From the solutions of the exterior von Neumann problem and the exterior Dirichlet problem, numerical examinations and comparison based on the usage of the new kernel and the usual kernel are presented. It is proved that the usual kernel cannot be used for the case in which the loadings on the contour are not in equilibrium. A particular exterior Dirichlet problem for an infinite plate with an elliptic inclusion is considered. Resultant forces and moment are applied on the inclusion. In the problem, one must assume some additional translation and rotation for the inclusion that are determined by the applied loading condition.