On asymmetrical equilibrium states of annular plates under normal pressure

The unsymmetrical buckling of annular plates with an elastically restrained edge which are subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of plate geometry (ratio of inner to outer radii) and boundary on the buckling load is examined. It is shown, that for an annulus the buckling pressure and the buckling mode number decreases as the inner radius increases. It is shown that as the internal radius increases, the plate loses stability as the buckling pressure decreases, which also leads to the buckling mode number decrease.