On the differential equations of the linear theory of elastic shells

Abstract

Recent developments in the foundations of the linear theory of thin elastic shells have substantially contributed toward establishing a satisfactory system of differential equations for bending of shells. Among these, we mention in particular the derivations by Koiter [1], Naghdi [2], and Green and Naghdi [3]. The latter contains a derivation which is effected via suitable asymptotic expansion of the three-dimensional equations of the classical theory of linear elasticity and leads to a system of shell equations equivalent to those in [1] and [2]. These shell equations involve only symmetric resultants and couples and symmetric shell-strain measures and conform to all invariance requirements appropriate to the linear theory. References to earlier and related contributions on the subject may be found in the references already cited, as well as in [4].