A couple-stresses elastic solution of an infinite tension plate bounded by an elliptical hole

AbstractCouple-stresses solutions are obtained for an infinite tension elastic plate bounded at the interior by an elliptical hole with the static equilibrating tractions. The nominal tension in the plate is uniform along the major axis. The selection of the Mathieus' functions and the form of weighting functions in the boundary conditions match a particular class of boundary values which reduces upon limiting processes to three special cases. These cases are ones with free stresses on the interior boundary: The couple-stresses solution for the degenerate circle, the couple-stresses solution for the degenerate crack, and the classical solution for the elliptical hole. Of particular interest is the degenerate crack problem. The couple-stresses solution for the degenerate crack is the same as the classical one of the crack. This is true because couple-stresses are related to curvature; however, no curvature is induced in this crack problem