ON AN INTEGRAL SOLUTION OF THE ANTIPLANE SHEAR PROBLEM

The boundary integral equation method is used to solve the problem cor responding to antiplane shear deformation of a homogeneous and anisotr opic linearly elastic solid whose cross-section is bounded by an arbit rary (smooth) closed curve. The solution is found in the form of a sin gle-layer potential based on the principal fundamental solution of ant iplane shear. Uniqueness and existence results are established in the appropriate function spaces. An example of an elastic solid with an el liptic cross-section is used to illustrate the theory.