Finite element analysis of air supported membrane structures

This paper deals with the finite element analysis of closed membrane structures that contain an enclosed fluid such as air. The change in the fluid pressure resulting from the application of external forces is evaluated and taken into account in the formulation of the equilibrium equations. The membrane formulation presented avoids the need for local co-ordinate axes by using the isoparametric finite element plane as a material reference configuration. The membrane material is modelled using standard large strain hyperelastic constitutive equations. The volume of fluid is obtained by integrating over the membrane surface and Boyle's law is used to determine the changes in air pressure that result from changes in volume. Full linearization of the internal pressure forces and the resulting additional term in the tangent operator are derived. This new component leads to a full but rank one matrix and an algorithm to solve the resulting linear system is provided. A number of numerical examples using the theory presented are considered.