A MIXED BOUNDARY VALUE PROBLEMS OF A STRIP WITH A CRACK UNDER THE CONCENTRATED BENDING AND TORSIONAL MOMENTS

The mixed boundary value problem of the thin plate is analyzed for a strip under concentrated bending and torsion. The strip has a part of the boundary where the displacement is constrained, and a crack initiating from an end of the constrained part. A rational mapping function which maps the strip with a crack into a unit circle and the complex stress functions for the deflection are used. The first derivative of the complex stress function is obtained in a closed form without integral term. The stress distributions before and after crack initiation, and the stress intensity factors of the thin plate for the bending and torsional modes are obtained from short to long cracks. The stress intensity factors are compared with those of other strips which are different in the constrained degree of the strip edge, and the effect of Poisson's ratio is studied.