By Gernot Beer

The booklet offers the state-of-the-art in isogeometric modeling and exhibits how the tactic has advantaged. First an advent to geometric modeling with NURBS and T-splines is given via the implementation into software program. The implementation in either the FEM and BEM is discussed.

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In this way, MIGFEM is much faster than using Matlab NURBS implementation. fem contains FEM M files to solve the same problems solved with IGA. Used as reference solution to check IGA implementation. msh). geo. fem-util contains some FEM related functions (Chessa (2002)) which are used in an IGA context (Gauss quadrature for instance). @patch2D contains classes and methods implementation for multi-patch isogeometric analysis. nurbs-geopdes is where the NURBS toolbox locates. We use the order elevation provided by this toolbox to perform k-refinement.

In Scott et al. (2013); Simpson et al. (2012) an isogeometric boundary element method was presented where no meshing is required at all allowing CAD models to be used directly for analysis. Shell and plate problems are another field of which IGA has demonstrated beneficial properties over conventional approaches Beirão da Veiga et al. (2012); Benson et al. (2010b, 2011, 2013); Echter et al. (2013); Kiendl et al. (2009); Uhm and Youn (2009). The smoothness of the NURBS basis functions allows for a straightforward construction of plate/shell elements.

4 Post-processing We present here a simple technique to visualize the IGA results that reuse available visualization techniques for finite elements. For the sake of simplicity, only 2D cases are considered here. In the first step, a mesh consisting of four-noded quadrilateral (Q4) elements is generated, see Figure 11. P. Nguyen and S. Bordas (a) NURBS mesh (b) approximate Q4 mesh (c) stress visualization on a refined mesh Figure 11: Exact NURBS mesh (top left) and approximate Q4 mesh (top right) for visualization purpose.

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