Plate Models for Buckling Analysis

The Föppl-von Kármán equations are widely used to model the buckling of thin elastic sheets. We demonstrate two significant shortcomings of these equations when used to analyse the pre- and post-buckling behaviour of inflated circular sheets. Specifically, we show that the equations (i) over-estimate the sheets' overall stiffness, and (ii) that they predict non-axisymmetric buckling to occur with a universal azimuthal wavenumber, independent of the sheet thickness, in contrast with experimental observations. We identify the origin of these shortcomings and demonstrate that they can be alleviated by using the nonlinear, large-strain Koiter plate model.