Asymmetric bifurcations in a pressurised circular thin plate under initial tension

It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl–von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.

► A coordinate-free formulation for the FvK plate bifurcation equations in displacements for the case of out-of-plane loads.
► A non-trivial extension of the edge-buckling phenomenon investigated in a series of recent papers by the author and his associates.
► A numerical investigation of localised wrinkling observed in pressurised thin plates, taking into account the effect of initial tension as well.