Equivalence between single-layered and certain multilayered shells.

Abstract

The concept of exact equivalence between a shell of multiple isotropic layers with equal Poisson's ratios and a single-layered shell is discussed. Exact equivalence is also noted between multilayered shells, the layers of which have properties symmetrically disposed about a middle surface, and sandwich shells with nonshear-deformable cores. The equivalence for problems of stress analysis, vibrations, and stability is defined in order to clarify the limitations on the concept. For multilayered shells which do not have an exactly equivalent shell, it is shown that single-layered shell theory can be used as an approximation for multilayered shell theory when coupling between bending and extension is small. However, when coupling is large, the approximation may yield inaccurate results, especially for stability and vibration problems. Thus, the application of the approximation to problems in which coupling occurs should be made with caution. A numerical example of the stress analysis of an axisymmetrically loaded circular conical shell leads to the conclusion that the approximation yields essentially exact results for this shell. By use of the approximation, results which were about 10% too high were obtained from a stability analysis of the previously mentioned circular conical shell.