Nonlinear static analysis of multi-segmented toroidal shells under external pressure

Abstract

This paper investigates the nonlinear static responses of multi-segmented toroidal shells with egg-shaped cross sections. The discontinuity effect in terms of displacement and the slope at the toroidal shell edge must be constrained by the Lagrange multiplier technique. The structural shape of the multi-segmented toroidal shells can be described by the differential geometry of the shell with the six-center-combined toroidal shells. The energy functional of the multi-segmented toroidal shells can be written in the appropriate form based on the principle of virtual work. The numerical results of the displacement responses and the volume change can be obtained by the nonlinear finite element method via the fifth-order polynomial shape function and a direct iterative method. In this study, the Lagrange multiplier is the internal force at the toroidal shell junction sustaining the smooth curve of the multi-segmented toroidal shells under several loads. Finally, the results of the volume change and the displacement responses for various geometric parameters are presented and discussed.