An elastic strip with a crack: an exact solution

A method of solving the problem for an infinite elastic strip with a transverse crack located on the vertical axis of symmetry is proposed. The solution is sought in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. The solution method does not depend on the type of homogeneous boundary conditions on the sides of the strip. To solve the problem, a function is constructed from the Papkovich–Fadle eigenfunctions that allows an analytical continuation outside the crack into the entire strip. The analytic continuation is constructed using the Borel transform. The solution sequence is shown using the example of an even-symmetric problem for a free strip with a central crack, on the sides of which normal stresses are specified.