Numerical analysis of large axisymmetric deformations of thin spherical shells

Abstract

Nonlinear difference equations for the numerical analysis of large axisymmetric deflections of thin linearly elastic and isotropic spherical shells a r e presented. Surface loading, temperature, and shell thickness may vary along a generator and, in addition, temperature may vary through the thickness. The difference equations, which govern a s t ress function and the rotation of a meridional tangent, are written in a convenient matrix form and solved by combining an iterative scheme with a direct elimination method. The general theory is programmed on an IBM 7090 digital computer, and important aspects of the input-output formats are explained. A nonclassical problem involving a deep spherical shell of variable thickness subjected to thermal, pressure, and edge loading is solved by means of the computer program. For this problem it was found that linear theory generally gave very conservative results. In addition, the problem of a spherical shell subjected to a concentrated load at the apex is treated, and certain of the numerical results a r e verified experimentally. lem indicate that within the framework of large deflection theory it is often necessary to carefully dist iny ish between inward and outward bending. Overall results for this prob