Weak Dirichlet boundary conditions for trimmed thin isogeometric shells

Abstract

Computer-aided design-based NURBS surfaces form the basis of isogeometric shell analysis which exploits the smoothness and higher continuity properties of NURBS to derive a suitable analysis model in an isoparametric sense. Equipped with higher order approximation capabilities the used NURBS functions focus increasingly on rotation-free shell elements which are considered to be difficult in the traditional finite element framework. The rotation-free formulation of shell elements is elegant and efficient but demands special care to enforce reliably essential translational and rotational boundary conditions which is even more challenging in the case of trimmed boundaries as common in CAD models. We propose a Nitsche-based extension of the Kirchhoff–Love theory to enforce weakly essential boundary conditions of the shell. We apply our method to trimmed and untrimmed NURBS structures and illustrate a good performance of the method with benchmark test models and a shell model from engineering practice. With an extension of the formulation to a weak enforcement of coupling constraints we are able to handle CAD-derived trimmed multi-patch NURBS models for thin shell structures.