A new method for the connection of non-conforming NURBS patches in isogeometric analysis

The main objective of isogeometric analysis is the use of one common data set for design and analysis. Geometrical models usually consist of multiple NURBS surface patches with non-matching parametrizations along common edges. The ability to handle non-conforming meshes is essential for isogeometric finite element systems to avoid manipulations of the geometry model. In general two possible strategies exist. The first one is to enhance the weak form of the potential with additional terms to constrain the deformations of adjacent edges to be equal, e.g. with the Lagrange Multiplier method. The second one is to establish a relation between the deformations of adjacent patches. Thus, superfluous degrees of freedom are condensated out of the system and the patches are connected naturally by shared degrees of freedom. No alteration of the weak form is necessary which simplifies the implementation in existing finite element systems. For adjacent edges with hierarchic knot vectors an analytical solution exists. In the general case of non-hierarchic knot vectors it is not possible to find an analytical solution. This contribution presents a new numerical method to establish this relation. A collocation along the connection line links the deformations of adjacent patches. A theoretical derivation of the method is given and the choice of the collocation points is investigated. Numerical studies compare the new method with the Lagrange Multiplier method and show its applicability. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)