Bending and Stability of a Thin Plate under Vacuuming Its Surfaces

Abstract

The effect of mean excessive pressure on the cylindrical bending of a plate is studied. An increase in this pressure leads to a decrease in deflection and vice versa. In the first case, the plate shape is stabilized under the action of longitudinal forces; in the second case, it is destabilized. The critical value of the mean pressure, upon achieving which an unlimited increase in the linear solution takes place, is determined. The dependence of the effect of the mean pressure on the bending on the boundary conditions, as well as on the ratio of pressures at the surface of the plate and at its edges, is shown.