Nonlinear Finite Element Analysis of Inflatable Prefolded Membrane Structures under Hydrostatic Loading

Abstract

Due to their flexibility shell or membrane like structures subjected to gas or fluid loading or gas/fluid support undergo large deformations. In order to describe this deformation dependent loading, where value and direction of the pressure loading are a function of the current configuration of the shell structure, the gas or fluid volumes, which are enclosed by the thin walled structure, have to be considered for the appropriate constitutive equations. Then the numerical formulation of the fluid or gas loading can be derived via an analytical meshfree description for the fluid/gas, which yields a special structure of equations involving the change of the gas or fluid volume respectively the change of the wetted part of the shell surface, see [2, 11–13]. This procedure finally leads to the so-called load-stiffness matrix, to which (in the case of enclosed gas/fluid volumes) several rank updates describing the coupling of the fluid or gas with the structural displacements in addition to the deformation dependence of the pressure load [15] are added. The numerical examples of e.g. (a) deploying simply folded membrane structures and (b) multi-chamber structures containing fluid and air in arbitrary combination demonstrate, how the simulation of structures with static gas and fluid loading or support can be efficiently performed without discretizing the fluid respectively the gas.