Large displacement analysis of ellipsoidal pressure vessel heads using the fundamental of differential geometry

Abstract

This paper presents an investigation of the large displacement analysis of ellipsoidal pressure vessel heads, based on the membrane shell theory. The strain components of deformed shell configurations could be obtained by using the fundamental knowledge of differential geometry. Energy functional of the ellipsoidal shell was derived from the principle of virtual work, which is expressed in the appropriate forms. Based on the nonlinear finite element procedures, the nodal displacements of the shell configuration were numerically obtained. Analytical method for the small displacement was derived in order to validate the numerical results obtained from the FEM. Interesting features from parametric study of normal and tangential displacements for arbitrary shapes of ellipsoidal shells are presented and discussed. It is revealed that the point of zero normal displacement for arbitrary shapes of ellipsoidal shells is always the same point which is independent of the applied internal pressure and thickness of shell. Furthermore, there exists the maximum point of tangential displacement and it is always at the same points of the radial distance when the internal pressure and thickness of shells are varied.