Perturbation method in the problem on a nearly circular hole in an elastic plane

The perturbation method is used to construct the solution of the plane elasticity problem for a plane with a curvilinear nearly circular hole. An algorithm for calculating any approximation represented as a Cauchy type integral depending on all preceding approximations is given. The complex potentials of the first approximation are obtained for an elliptic hole and a curvilinear hole whose boundary deviates from the unit circle in the radial direction according to the cosine law. An example of elliptic hole is used to analyze the error in the first approximation of the stress concentration factor by comparing it with the exact solution. The influence of the hole shape on the distribution of circular stresses on the boundary is studied.