Rotation free shell formulations [1, 2] provide an interesting and effectiveoption for the FE analysis of Kirchhoff-Love type shells. Due to theirwell defined discretization parameters, which consist only of displacements,they are especially advantageous for geometrically nonlinear structuralanalysis (static and dynamic) and shape optimization of thin shell structures,as no difficulties occur in a unique definition of rotational degrees offreedom during large deformations. The proposed CEG element (CurvatureCalculation through Enhanced Geometry) is a multi-purpose general rotationfree element [1]: Isoparametric displacement elements (triangles and quadrilaterals)are used as basic geometric description and to determine the membrane strains.The calculation of curvature is based on discrete nodal directors, whichare assigned to each node and determined by the geometry of a surroundingelement patch (Fig. 1). With their help, an additional rotation field isgenerated within each element in order to determine the otherwise missingcurvature information. The kinematics is formulated completely nonlinear.One basic advantage of this element formulation is the modular technologyallowing for adding bending stiffness to an initial membrane model usingthe same geometrical discretization and, thus, supporting the entire designprocedure: E.g., it can be favourable to design the shape of a shell structurein such a way, that it bears its main load case only by membrane action.This geometry can be obtained with a form finding procedure [3] using onlymembrane elements. Yet, as other load cases will generally occur in thelifetime of this structure, it is nevertheless necessary to check its loadbearing capacities in a series of structural analyses using shell elements(see Fig. 2 for an illustration). It is furthermore possible, to additionallyoptimize the structure according to various objective functions and constraintsby applying free form optimization using exact semi-analytical derivatives[4]. If the CEG rotation free shell element is used, the original discretizationcan be retained at all design steps and, hence, a time consuming changefrom membrane to shell elements is avoided. The efficiency and effectivityof the proposed element formulation is shown in several examples ranginglinear static to nonlinear dynamic analysis and optimization.     «

Rotation free shell formulations [1, 2] provide an interesting and effectiveoption for the FE analysis of Kirchhoff-Love type shells. Due to theirwell defined discretization parameters, which consist only of displacements,they are especially advantageous for geometrically nonlinear structuralanalysis (static and dynamic) and shape optimization of thin shell structures,as no difficulties occur in a unique definition of rotational degrees offreedom during large deformations. The proposed CEG eleme...     »