Flexural problems of a thin plate with a curved crack

Abstract

This paper, based upon the elementary theory of thin elastic plates, deals with the solution of three types of boundary value problems, namely the first, the second and the mixed type, for an infinite plate with a cut along a circular arc. It is assumed that the stress state at infinity is uniform. Complex variable analysis is used throughout, and each problem is reduced to Hilbert problems for two unknown functions, the solution of which is obtained in closed form. The flexural stress in the neighborhood of the crack is found to have the singularity of the order of r-1/2, r being the radial distance from the crack point, in cases of the first and second problems, whereas it is shown to be of an oscillating character with singularity of the order of r-3/4 in the case of the mixed problem. Numerical calculations are carried out for the cases of plain bending about the axes of symmetry and for a semi-circular cut.