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Weakly enforced boundary & coupling constraints for isogeometric rotation-free thin shells

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 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 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 shell models 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. Adequate stabilization of the formulation ensures an overall smooth solution which is demonstrated for matching and non-matching multi-patch models.

Author(s):

Martin Ruess    
Delft University of Technology
Netherlands

Yujie Guo    
Delft University of Technology
Netherlands