Shells of revolution with local plasticity

Abstract

A nonlinear finite element model that is suitable for the static analysis of shells of revolution with local plasticity is developed. Actually, shells of revolution always exhibit local deviations, like a cutout, a junction, and/or an imperfection. The stress concentration caused around a local deviation may make the material plastic in the surrounding region. The analytical model consists of three different types of shell elements: rotational, general, and transitional. The rotational shell elements are used in the region where the shell is axisymmetrical, and the general shell elements are deployed in the region of the deviation. The transitional shell elements are inserted between the two distinctively different types of elements to achieve continuity of displacement fields. Only the general shell element possesses the material nonlinear properties to capture the localized plasticity. A simple description of plastic behavior based on elastic-plastic behavior, the Von Mises criterion, the Prandtl-Reuss flow rule, and a layered structure, developing plastification through the thickness of the general shell, is used. The stress components at appropriately chosen station points covering the entire volume of the element are stored during the computation. A check is made for initial yielding in the general shell elements at the end of each step of loading. The results of three numerical studies elucidate the localized nonlinear material behavior in a rotational shell structure. In the first example, an axisymmetric junction problem is studied to check the technique against published results. Then, in the last two examples, a cylindrical shell with a circumferential line crack and with a circular cutout are studied. Since the selection of the size of the substructure and the number of harmonics are very important for the localized plasticity problem in the rotational shell, detailed convergence studies are presented. It is shown that the local-global analysis is an attractive alternative to the entirely general element style analysis for axisymmetric shell structures with local imperfections.