Analytical and Numerical Analyses for a Variety of Submerged Hemi-Ellipsoidal Shells

Abstract

This paper concerned an analytical method to obtain exact solutions for displacements of submerged hemi-ellipsoidal shells. Based on the linear membrane theory, the membrane forces and strain components were defined in terms of the radius of a parallel circle. General solutions for normal and tangential displacements were established, which could be written in the simplest form when considered at the apex and equatorial points. To investigate the accuracy of the results, a finite-element modeling technique was used to verify the analytical solutions. The fundamentals of differential geometry and the principle of virtual work were used to develop the stiffness matrix for nonlinear finite-element procedures. This led to the numerical results for validation of the analytical solutions. The effect of shape ratios, thickness, and seawater depth on the forces and displacements of submerged hemi-ellipsoidal shells were also presented in this study.