Green's Function for Mixed Boundary Value Problem of Thin Plate

Abstract

In this study, the Green's function of a point dislocation for the mixed boundary value problem of a thin plate is derived and then employed to analyze the interaction problem between a partially bonded rigid inclusion and a line crack in an infinite plate under uniform bending moments at infinity. A rational mapping technique and the complex stress function approach are used in the derivation. Based on the method of analytical continuation, the problem of obtaining the stress functions is reduced to a Riemann-Hilbert problem. Without loss of generality, the numerical results are demonstrated for a square rigid inclusion with a debonding. The stress intensity factors of crack tips and the stress intensities of debonding tips are shown for various parameters.