An approximate theory for geometrically nonlinear thin plates

An approximate theory of thin plates is developed that is based on an assumed displacement ®eld, the strains described by a Taylor series in the normal distance from the middle surface, the exact strains of the middle surface, and the equations of equilibrium governing the exact con®guration of the deformed middle surface. In this theory, the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of plates. This theory reduces to some existing nonlinear theories through imposition of constraints. Application of this theory does not depend on the constitutive law because, the physical deformation measure is used. It can also be applied when the response, loading and geometry of the plate are asymmetric and when the vibration mode number is not small. Predictions of membrane forces in a rectangular plate and of the equilibrium solution in a rotating disk are sample problems