Numerical and analytical solutions with finite strains for circular inflated membranes considering pressure–volume coupling

• Analytical and numerical solutions for an inflated circular membrane clamped at its rim were compared.
• The pressure–volume coupling included in the formulation takes into account the variation of the internal pressure.
• Analytical solution considering large strains in the pressure–volume coupled problems was developed.
• The numerical implementation of pressure–volume coupling for pneumatic structures was validated with analytical solutions.

The classical problem of the circular inflated membrane fixed at its rim and expanded under gas pressure is studied in this paper. Numerical and analytical solutions considering pressure–volume coupling are investigated. It should be pointed out that the application of the analytical solutions described in this section to closed chambers considering pressure volume coupling requires the adoption of recursive solutions scheme. The deformed configuration and volume are updated followed by the pressure update through the ideal gas law. The analytical solutions presented in the literature for this problem consider only the presence of small strains. In the present study the solutions given by Hencky, Fichter and Campbell are studied. A novel finite strain solution is derived, as an extension of Fichter׳s solution. The numerical solution is based on the finite element method and also considers finite strain kinematics. The results of numerical and analytical models for an enclosed circular membrane are compared, where the effects of small and finite strains with or without the consideration of the pressure–volume coupling are highlighted.