An Assessment of Classical and Refined Plate Theories Derived From the Principle of Virtual Displacements

Abstract

Classical and refined plate theories can be derived either by postulating the existence of a Cosserat surface (direct approach) or by reducing a set of three-dimensional equations of continuum to a two-dimensional system (reduction techniques). In the first case, it is a priori assumed that the plate can be represented by a two-dimensional surface, whose deformation is described by translations and additional kinematical degrees of freedom. The additional degrees of freedom must in a later stage be physically interpreted, f. e. as mid-plane rotations. Constitutive relations are formulated between these kinematical degrees of freedom and corresponding kinetic degrees of freedom, which are in most cases physically interpreted as forces and moments.