Modern conceptions of plate theory

Abstract

The paper is concerned with history and present state of the art of the sixth-order plate theories originally developed by Reissner, Hencky, and Bolle. In contrast to the existing interpretation of these theories as versions of the non-classical shear deformable plate theory, an attempt is made to demonstrate that, under proper transformation, the sixth-order theory can be qualified as a modern form of the classical plate theory. To support this conception, physical inconsistency of the existing fourth-order classical plate theory is demonstrated, while equations of the sixth-order theory are derived in a traditional straightforward way not requiring variational calculus and providing the plate theory consistent from both mathematical and physical standpoints. Analysis and examples are presented to show that both the biharmonic equation to which Kirchhoff plate theory is reduced and the second-order boundary layer equation derived by Reissner are non-separable parts of one and the same theory that is proposed to be referred to as the classical plate theory.