Mixed Boundary Value Problem of Plate with Crack

Abstract

A semi‐infinite plate, of which a part on the boundary is rigidly stiffened and in which a crack initiates from an end of the stiffened edge as a problem of a mixed boundary value of thin plate bending, is analyzed. The problem is solved by a complex variable method which uses a rational mapping function. Two analytical methods are described: one method can apply to general loads and the other can apply when the free boundary, even partially, exists. These methods give a solution in a closed form for a shape represented by the rational mapping function. Uniform bending and torsion are considered as loads. Bending moment distributions before and after crack initiation, and the stress intensity factor are investigated for crack length, stiffened edge length, and the Poisson's ratio.