On generalized two-dimensional plate theory—II

Abstract

In elaboration of a recently proposed procedure for the derivation of two-dimensional shell theory from three-dimensional elasticity theory the special case of a flat plate is considered explicitly. The starting point of the work is a suitable version of elasticity theory including moment as well as force stresses. It is shown that a certain straightforward but not previously considered reduction of three-dimensional equilibrium and compatibility equations leads to suitable two-dimensional equilibrium and compatibility equations, while leaving the three-dimensional aspects of the problem in the form of a system of integro-differential constitutive equations. The derivation of two-dimensional constitutive equations then is one involving parametric expansion or iteration, in conjunction with the stipulation of smallest characteristic length large compared to plate thickness.