Coupling of non‐conforming NURBS patches with the weak substitution method

Abstract

AbstractIsogeometric analysis unifies the data model for the description of the geometry for design and analysis. The analysis is altered towards compatibility with the geometry model used in the design work flow. The basis functions of the geometry descriptions are used to approximate all unknown quantities in the numerical simulation. The most common geometry model in design industry is NURBS surfaces. The properties of NURBS surfaces do not allow local refinement. Geometrical models in industrial applications generally consist of several NURBS patches, which usually neither have conforming knot vectors nor the same degree. Thus, the control points do not coincide and a connection by shared control points is not possible. Special methods to avoid mutual refinement are necessary. This works presents a new method for the coupling of non‐conforming patches. A relation between the deformations of control points having influence on shared edges is established. This relation allows expressing the deformations of a set of slave control points as a function of the deformations of the appropriate master control points. Thus, the slave control points, as well as the associated degrees of freedom can be removed from the global system of equation. The method can also be used for nonlinear computations without additional effort. The derivation of the proposed relation is shown. Numerical examples show the high accuracy of the presented method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)