Asymptotically Accurate Non-linear Analysis of Inflatable Structures
Ramesh Gupta, B.; Harursampath, D.
Indian Institute of Science

The focus of this work is on the development of an intrinsic formulation of an asymptotically correct theory for inflatable structures. The problem is both geometrically and materially nonlinear. The geometric nonlinearity is handled by allowing for finite deformations and generalized warping while the material nonlinearity is incorporated through a recently validated hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness-to-wavelength ratio as small parametrs, begins with three- dimensional nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional membrane analysis. The through-the-thickness analysis provides consti- tutive relation between the generalized two dimensional strain and stress tensors for the membrane analysis and a set of recovery relations to approximately express the three-dimensional displacement, strain and stress fields in terms of two-dimensional variables determined from solving the equations of the membrane analysis. Numerical examples are presented to compare with existing analytical, semi-analytical and finite element solutions. Results based on this model will be demonstrated for specific inflatable structures.