Couple-Stress Solution to an Infinite Plate Bounded by an Elliptical Hole with Static Equilibrating Tractions

摘要

Couple-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 minor 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. The first two cases are ones with free stresses on the interior boundary; the couple-stresses solution for the degenerate circle, and the classical solution for the elliptical hole. The third case is the degenerate crack solution with free normal stress and couple stress but non-vanishing shearing stress on the interior boundary. By super-imposing the current solutions on the solutions obtained in another document AFOSR-TR-70-2500 couple-stresses solutions for an infinite elastic plate bounded at the interior by an elliptical hole with the static equilibrating tractions under various biaxial fields of load can easily be obtained. (Author)