On Asymptotic Expansions and Error Bounds in the Derivation of Two‐Dimensional Shell Theory

Abstract

Known results on asymptotic two‐dimensional equations for circular cylindrical shells, including the effects of transverse shear and normal stress deformation, are supplemented by upper‐ and lower‐bound determinations of influence coefficients, using minimum‐potential and complementary energy principles in conjunction with asymptotic‐expansion results. The new bound analysis shows that the consequences of the asymptotic two‐dimensional theory are in exact agreement, except for terms which are small of higher order, with the corresponding consequences of three‐dimensional theory, for some classes of edge conditions. The analysis also shows the nature of the differences between results of two‐ and three‐dimensional theory, as a function of geometrical and elastic parameters, where this difference is of importance because of the effect of a St. Venant boundary layer.