A cracked infinite Kirchhoff plate supported by a two-parameter elastic foundation

This paper presents a full-field solution for the linear elasto-static problem of a homogeneous infinite Kirchhoff plate with a semi-infinite line crack resting on a two-parameter elastic foundation. The same model describes the problem of a cracked plate equi-biaxially loaded in its mid-plane by a constant normal force and, as a limiting case, the problem of a cracked spherical shell. The full-field solution is obtained in closed form through the Wiener-Hopf method in terms of Fourier integrals. The stress-intensity factor (SIF) for the case of symmetric and skew-symmetric loading conditions are obtained and the role of the soil parameters discussed. In particular, it is shown that a purely local model (Winkler) is unable to provide a safe-proof design limit.