“Upgrading” membranes to shells—The CEG rotation free shell element and its application in structural analysis

A multi-purpose general rotation free element for the analysis of thin Kirchhoff–Love type shells is presented: Isoparametric displacement elements are used as basic geometrical description and to determine the membrane strains. Calculation of curvature to determine bending strains is based on discrete nodal directors, which are assigned to each node and determined by the geometry of the surrounding elements. The kinematic is formulated completely nonlinear. The technology is modular allowing for adding bending stiffness to an initial membrane model using the same geometrical discretization and, thus, supporting the entire design procedure from form finding to ultimate load or dynamic analysis of thin shells. Different examples ranging from static wrinkling analysis of a membrane to nonlinear dynamic analysis of a thin metal shelter show the multitude of possible applications.