The elastic plate containing two collinear transverse edge-cracks (Q1073640)

The paper solves the problem, in a closed form, of the stress distribution in an infinite plate containing two collinear and transverse edge-cracks, subjected to an axial loading at infinity. The distribution of stresses and displacements all over the cracked plate was effectively solved by applying the method of isostatics, as it has been developed by the author in J. Appl. Mech. 26, 227-234 (1959). The solution of the problem was formulated as a Boussinesq-type problem, where the ligament between the symmetric edge cracks corresponds to the constant displacement zone of the rigid punch. The stress distribution in the cracked plate was expressed by an analytic function of complex variable, which represents the field of isostatics (i.e. the principal stress trajectories). The advantage of the method over all other existing solutions is that it gives the components of stresses all over the field with the same degree of accuracy, based on a closed-form type of solution. These stresses are given in graphical form along characteristic sections of the plate. Therefore, the method is proved effective for solving completely the problem of externally cracked plates with the same accuracy, as the closed-form solution of an internal crack. The advantages of this fact may be appreciated when one has to find out crack opening displacements all over the lengths of the cracks and, in general, needs data outside the close neighbourhood of the crack tips.