Bending of a Thin Plate in a High Pressure Field

A linear theory of static cylindrical bending of a thin plate is constructed without using the Kirchhoff hypotheses. Transverse shear, thickness compression, and the resulting longitudinal force are taken into account. In view of changes in the areas of both surfaces during bending, the transverse distributed force is determined. It is assumed that the average pressure on the plate is several orders of magnitude greater than the pressure difference. Bending is considered under the conditions of a plane strain state and a stress state.