Stressed state of polygonal plate with central circular hollow and two linear cracks

A plane elasticity theory solution is obtained and illustrated for the cases of a hexagonal plate containing a central circular hole subjected to uniformly distributed internal and external pressures P1 and P2, and a hollow cylinder with two cracks. The ratio of the bee-line between the hole center and the external contour to the hole radius (r/b) is found to have significant impact on the stress concentration. For the case of r/b of not greater than 0.4 and a crack length of less than 0.1(b - r), the presence of the crack is not found to effect the stress concentration near the holes. Formulas are presented which determine the stressed state due to P1 (given P2) or to P2 (given P1). (R.R.)