A nonlinear stability analysis of an incompressible elastic plate subjected to an all-round tension

Abstract

When an incompressible elastic plate is subjected to an all-round tension, linear stability analysis predicts that it will become neutrally stable with respect to both extensional and flexural modes and to all wavenumbers when the tension is twice the shear modulus. In this paper a weakly nonlinear analysis is conducted to determine the post-buckling states when the tension deviates from its neutral value by a small amount. It is found that such a prestressed plate with any given thickness can bifurcate into an infinite number of post-buckling states, and that only one such state is sinusoidal, the rest being non-sinusoidal. All the post-buckling states are found to be stable with respect to small perturbations.