Bending of a Thin Reissner Plate With a Through Crack

Abstract

The title problem was first considered by Knowles and Wang (1960) and was shown to be related to the solution given by the classical plate theory. This solution is actually the outer solution of a singular perturbation problem, and therefore is valid only away from the crack-tip region. Within a boundary layer of order h/a, where h is the plate thickness and a is the half-crack length, the two theories differ considerably. In this study the leading order solution is obtained for h/a - 0 and it is shown that the limiting stress intensity factor given by the Reissner plate theory is more than 50 percent higher than the asymptotic result (1 + v)/(3 + v) which is obtained from the displacement field as given by the classical plate theory.