Green's Functions of Thin Plate Bending Problem under Fixed Boundary

Abstract

The Green's functions of a point dislocation, a concentrated moment, a normal point force, a couple moment, and a couple bending force applied to an infinite plate with an arbitrarily shaped hole under a displacement boundary condition are derived in this paper. The closed-form stress functions are obtained by using the technique of the rational mapping function and the complex stress function approach. In the derivation, the analytical continuation and Cauchy integral are used for the different actions. Without loss of generality, some calculated results are shown for a square hole under a fixed boundary. The solutions show that the stress functions have different orders of singularity for the different actions. In order to illustrate the stress level due to bending moment and shear force clearly and efficiently, the effective stress of thin plate bending is shown.