Finite Deflections of Circular Membranes

Abstract

The behavior of membrane-like structures is of interest in conjunction with problems concerning slack diaphragms, inflatable structures, explosive forming of metals, interpretation of hydrostatic bulge tests, and continuous analysis of cable nets. For rotationally symmetric loadings of initially flat elastic circular membranes (the subject of this note), the Foppl-Von Karman equations are usually used to carry out the stress and deformation analysis. These equations are valid for moderate rotations and deformations and small strains. The membrane form of the equations given by Reissner represents a generalization of the Foppl-Von Karman theory to the case of arbitrarily large rotations and deformations, while retaining the small strain assumption. The purpose of the present work is to obtain some solutions to the Reissner membrane equations and compare these results to those previously found from the Foppl-Von Karman equations.