Singular solutions for an anisotropic plate with an elliptical hole

A solution of the bending problem for a plate with an elliptical hole subjected to a point force (a singular solution) is obtained using the engineering theory of thin anisotropic plates and Lekhnitskii’s complex potentials. The solution is constructed by conformal mapping of the exterior of the elliptical hole onto the exterior of a unit circle with evaluation of the Cauchy-type integrals over closed contours. Different versions of the boundary conditions on the holw contour are considered. In the limiting case where the ellipse becomes a slot, the solution describes the bending of a plate with a rectilinear crack or a rigid inclusion.