Large displacement analysis of egg-shaped containment shells using Lagrange multipliers

In this paper, a large displacement analysis of three-center-combined spherical shells, used as egg-shaped containment structures, is performed using the first and second fundamental forms of the shell surface with two different radii of curvature. The energy functional of the three-center-combined spherical shells system is derived using a variational formulation, and is written in the appropriate form to reduce the computation time in an iterative procedure. The numerical results in terms of displacement, membrane stress, and bending moment resultants are obtained by nonlinear finite element analysis with a fifth-order polynomial shape function. At the spherical shell edge, the Lagrange multipliers technique is used to enforce the discontinuity effect. The main conclusions are that the displacement responses, membrane stress, and bending moment resultants depend on the geometric parameters of the three-center-combined spherical shells. The Lagrange multipliers correspond to the internal forces due to the displacement and the slope at the shell edge in order to sustain the smooth curve for deformed configuration of the three-center-combined spherical shells under uniform pressure. The volume capacity of the three-center-combined spherical shells are more than the spherical shells with a constant radius. Finally, the results indicate that the linear assumption is good enough for all practical purposes. However, the large displacement analysis becomes significant on the tangential displacement, meridional, and circumferential moments under the large value of uniform pressure.