A novel technique for removing the rigid body motion in interior BVP of plane elasticity

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.