Finding coefficients in the problem of a cylindrical shell with a circular cutout

Abstract

Abstract In the present paper a cylindrical shell with a circular cutout is considered. There have not yet been explicit formulas for the field of stresses and after reviewing some ideas of the derivation of the solution of this problem, the authors can present how this can be done. A new approach is based on the separation of variables in the basis function by Fourier decomposition and on the proof of reducibility of the system. This way has a strict mathematical foundation, and for the boundary condition in the form of axial tension the limit transition leads for the Kirsch problem, as expected. In this work a finding of coefficients for small parameter is illustrated and the limit transition is shown.