LAUSR

Abstract This paper investigates the behaviour of an underwater toroidal shell storage container filled with compressible fluid under constraint volume condition. The fundamental form of the surface is used to define the geometry of a toroidal shell under an initial unstrained state (IUS), reference state (RS), and deformed state (DS). In the reference state, it is assumed that the toroidal shell storage container has a circular cross section. In the deformed state, the displacements of the shell are assumed to be large. The energy functional of the underwater toroidal shell storage container can be established based on the principle of virtual work, and it can be rearranged in an appropriate form that can conveniently be implemented in a finite element formulation. The nonlinear static analysis of the toroidal storage container under external hydrostatic pressure can be performed by the nonlinear finite element method (FEM) via the fifth-order polynomials shape functions. The nonlinear responses under the variable water depth to cross-sectional radius, cross-sectional radius to wall thickness, and cross-sectional bend radii ratio are demonstrated and discussed. The results revealed that the change of internal pressure is indicated by the value of the Lagrange multiplier, which is calculated using the iterative method for finding the equilibrium configuration under the constraint volume requirement.