On the Inflation of a Plane Nonlinear Membrane

Abstract

The deformed configurations of an inflated flat nonlinear membrane are obtained by the minimum potential energy principle. The deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy of the deformed membrane are determined by Fletcher and Powell’s [1] method. The strain-energy-density function for the numerical calculations is assumed to have the Mooney form. The results for a particular case when the Mooney membrane reduces to the neo-Hookean membrane, agree with the previous results obtained by numerical integration of the corresponding equilibrium equations.