Isogeometric shell analysis with Kirchhoff–Love elements

A Kirchhoff–Love shell element is developed on the basis of the isogeometric approach [16]. NURBS as basis functions for analysis have proven to be very efficient and offer the great feature of exact geometric representation. For a Kirchhoff–Love shell element they additionally have the significant advantage that the necessary continuities between elements are easily achieved. The element is formulated geometrically nonlinear. It is discretized by displacement degrees of freedom only. Aspects related to rotational degrees of freedom are handled by the displacement control variables, too. A NURBS-based CAD program is used to model shell structures built up from NURBS and isogeometric analysis is performed on the same model without meshing. Different examples show the performance of this method and its applicability for the integration of design and analysis.