Energy Expressions and Differential Equations …. for Stress and Displacement Analyses of Arbitrary Cylindrical Shells

Abstract

Energy expressions and the related equilibrium equations and natural boundary conditions for the determination of the stresses in and displacements of uniform, thin-walled cylinders of arbitrary cross section loaded in an arbitrary manner by surface and edge forces and moments are presented. The derivations are based upon the Kirchhoff-Love assumptions of the classical theory of shells and are performed to within a degree of accuracy employed by Flügge in his derivation of the equilibrium equations applicable to circular cylindrical shells; hence, in terms of stress resultants, the exact, small-deflection equilibrium equations are obtained. Methods of simplification of the relations derived and of solution of the differential equations presented are indicated.