The weak substitution method – an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis

In this contribution, a mortar‐type method for the coupling of non‐conforming NURBS (Non‐Uniform Rational B‐spline) surface patches is proposed. The connection of non‐conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor‐product structure of NURBS surfaces. Thus, methods to handle non‐conforming meshes are essential in NURBS‐based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master‐slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given. Copyright © 2015 John Wiley & Sons, Ltd.