The Bending Stress in a Cracked Plate on an Elastic Foundation

Abstract

Classical Kirchhoff bending solutions for a normally loaded elastically supported flat plate containing a semi-infinite straight crack are obtained using an integral equation formulation. Because the effects of initial spherical plate curvature are related to those of an elastic foundation, the solution can be applied to the problem of a crack in an initially curved unsupported plate as well. The explicit nature of the stresses near the crack point is found to depend upon the inverse half power of the nondimensional distance from the point, r/(D/k)1/4, where D is the flexural rigidity of the plate and k the foundation modulus. The particular case of an infinite strip containing the crack along the negative x-axis and loaded by constant moments M* along y = ±y* is presented. The inverse half-power decay of stress is additionally damped by an exponential factor of the form exp(−λy*/2).