A critique of the classical theory of elastic thin shells

Abstract

Several theories in shell literature have as their basis the Love-Kirchhoff assumptions. (Ignoring the effects of transverse normal and transverse shear strains and also assuming the transverse normal stress to be zero). Although the derivation of these theories is based on the same assumptions, the stress strain relations in each theory differ by some displacement terms. The authors of these theories claim higher accuracy for their work because of some additional displacement terms contained in their equations. In this paper an attempt will be made to investigate the error due to the Love-Kirchhoff assumptions by using “Mathematical Exact Theory” of Zerna[1]. It will be shown that the claim of several authors for a more accurate theory is unjustified because the error inherent in the additional displacement terms. It will be also shown how as with Love-Kirchhoff assumptions consistent stress-strain relation must be formulated.