Application of perturbation-variation method in large deformation bimodular cylindrical shells: A comparative study of bending theory and membrane theory

Abstract

A bimodular material is a kind of material that presents two elastic moduli in tension and compression. In the existing researches, the bimodular effect of materials is rarely considered due to its complexity in analysis. In this study, the large deformation problem of bimodular cylindrical shells is analytically and numerically investigated, in which the typical issue in cylindrical shells, using bending theory or membrane theory, is comparatively studied on the basis of large deformation. First, the large deformation governing equations on bimodular materials model are established under bending theory and membrane theory. A new analytical method, perturbation-variation method, is then used to obtain the theoretical solutions under bending theory and membrane theory. The numerical simulation also validates the theoretical solution obtained. The results show that the shape of cylindrical shells and the bimodular effect of materials have important influences on the relationship of load vs. central deflection and subsequent occurred jumping phenomenon. The rational use of both theories depends on many factors. Specifically, when the circumferential length of cylindrical shells is far greater than the longitudinal length, it is more reliable to adopt the membrane theory instead of the bending theory to analyze large deformation problem of bimodular thin cylindrical shells.