On the nonlinear membrane approximation and edge-wrinkling

• The paper investigates edge-wrinkling of a uniformly stretched thin elastic plate subjected to uniform pressure.
• Nonlinear membrane equations are used for the pre-buckling state.
• Asymptotic formulae are obtained for the critical load and mode number.
• Analytical results compared with direct numerical simulations indicate good agreement.
• An analytical error estimate is provided for the effect of neglecting bending stiffness in the pre-buckling range.

The wrinkling of a uniformly stretched thin elastic plate subjected to a pressure acting perpendicular to its surface is re-visited. The problem is tackled under the assumption that the basic state can be adequately described by an appropriate nonlinear membrane analysis. That this simplification might be reasonable was suggested by recent related work in which numerical simulations showed that bending effects tend to be negligible for typical load levels that cause the initial axisymmetric deformation of the plate to bifurcate into an asymmetric mode. The effect of this seemingly unimportant change on the asymptotic description of the wrinkling instability is fully investigated here, and a direct quantitative assessment is made with earlier results in which the bending resistance of the axisymmetric deformation mode was accounted for.