On Refined Theories of Beams, Plates, and Shells

This paper deals with refined beam, plate, and shell theories which are based on the reduction of the three-dimensional elasticity theory by assuming an approx imation of the displacements through the thickness. Conditions which should be imposed on this approximation to provide the consistency of the theory are obtained. For brevity's sake the derivation is performed for a beam, the results being further generalized for plates and shells. A thick isotropic plate is considered as an example.