On the Loss of Stability of Symmetrical Equilibrium Forms of Circular Plates under Normal Pressure

The stability of axisymmetric equilibrium states of an isotropic non-homogeneous circular plate under uniform pressure is considered. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinates. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. It is shown that if the elasticity modulus decreases away from the center of a plate, the critical pressure for unsymmetric buckling is sufficiently lower than for a plate with constant mechanical properties. The folds in the narrow zone at the periphery of the lamina cibrosa (LC) of the human eye could be explained by the bucking of the axisymmetric state of the LC in the nonaxisymmetric state.