On the Stresses in a Plate Containing Two Circular Holes

Abstract

This note gives a theoretical solution to a plate containing two circular holes of equal size. The method of solution is to add to the given stress system a suitable biharmonic function which gives no stress at infinity. The parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the edges of the holes. Bipolar coordinates are used in the solution, by means of which explicit expressions are obtained for the parametric coefficients. Three fundamental stress systems are discussed in some detail, namely, the all‐around tension case, the longitudinal tension case, and the transverse tension case. Formulas of the stress along the edges of holes are derived and, in particular, values of maximum stress are calculated. The limiting case in which the holes are tangential is also discussed.