Antiplane contact problems of a half-space with a semielliptic hole

We consider the problem of a half-space with a stress-free semielliptic hole in the following two loading cases through antiplane contacts: (i) an antiplane shear contact applied through an infinitely long rigid strip bonded to a line on the surface of the half-space, and (ii) two collinear antiplane shear contacts applied through two infinitely long rigid strips. The integral transform technique for each problem is reduced to triple integral equations with cosine kernels and weight functions. Closed-form solutions of this set of triple integral equations are then obtained. Closed-form expressions are also obtained for the distribution of surface stress under the contacts and for the total pressure on the pressed area. Numerical results for displacements, surface stress, and total pressure are given in graph form.