Analysis of a spherical tank under a local action

Abstract

A spherical tank, being perfect as far as weight is concerned, is used in spacecraft, where the thin-walled elements (shells) are united by frames. Obviously, local actions on the shell and hence the stress concentration in the shell cannot be avoided. Attempts to make weight structure of the spacecraft perfect inevitably decrease the safetymargin of the components, which is possible only if the stress-strain state of the components is determined with a controlled error. A mathematical model of shell deformation mechanics is proposed for this purpose, and its linear differential equations are obtained with an error that does not exceed the error of Kirchhoff assumptions in the theory of shells. The algorithm for solving these equations contains procedures for estimating the convergence of the Fourier series and the series of the hypergeometric function with a prescribed error, and the problem can be solved analytically.