Boundary Conditions and Multi‐Patch Connections in Isogeometric Analysis

Abstract

Isogeometric analysis is a high‐continuity alternative to the standard finite element method. However, for practical application several issues remain to be addressed. This contribution discusses the imposition of Dirichlet boundary conditions as well as the connection between multiple patches. In particular necessary manipulations of the geometrical input data are provided. Dirichlet boundary conditions can be imposed in weak or in strong form. Due to the non‐interpolatory characteristics of NURBS surfaces weak imposition of Dirichlet conditions is a viable option which avoids local transformations. The connection of multiple patches can be realized in a weak manner by adding additional terms to the variational equations, for example by the Lagrange multiplier method or the perturbed Lagrangian method. Both base on the idea of multiplying the mutual deformations with an additional unknown to force the deformations on shared edges to be equal. The numerical treatment leads to different sets of equations. In contrast to strong inter‐patch connections, where coinciding control points share the same degrees of freedom, weak imposition allows for hanging nodes and therefore local refinement. The theoretical background and issues of implementation are given. Some numerical examples compare error norms for all mentioned methods and demonstrate that in particular cases a reduction of continuity leads to more accurate results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)