Green’s functions for an anisotropic thin plate with a crack or an anticrack

Abstract

Based on the octet formalism established by the authors, Green’s functions for an infinite anisotropic elastic thin plate with a Griffith crack or an anticrack (rigid line inclusion) are studied. The plate can be laminated or consist of a continuously inhomogeneous material in the thickness direction. Two systems of problems of the plate under non-self-equilibrated loads are solved. The first is associated with discontinuous in-plane displacements and slopes, in-plane concentrated forces and out-of-plane concentrated moments. The second is associated with a transverse concentrated force. The Green functions for an infinite plate with a crack or an anticrack and the surface Green functions for an infinite plate with a crack are obtained in an exact closed form. The surface Green functions and associated stress resultants at any point throughout the line where the crack is located are presented in a real form. The intensity factor of membrane stress resultants and bending moments are obtained in a real form for the Griffith crack subjected to concentrated loads.