We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and immersed boundary analysis. We use the principle of B-spline subdivision to derive a local refinement procedure, which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions. We test hierarchical refinement of NURBS for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases. Using the B-spline version of the finite cell method, we illustrate the potential of immersed boundary methods as a seamless isogeometric design-through-analysis procedure for complex engineering parts defined by T-spline CAD surfaces, specifically a ship propeller and an automobile wheel. We show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features.
|Original language||English (US)|
|Number of pages||35|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Dec 1 2012|
Bibliographical noteFunding Information:
This work was accomplished during a three month visit of Dominik Schillinger at the Institute of Computational Engineering and Sciences (ICES) in summer 2011, for which financial support from the Centre of Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) of the Technische Universität München is gratefully acknowledged.
The ICES team gratefully acknowledges the support of the following research grants and contracts: ONR Grant N00014-08-1-0992, ARO contract W911NF-10-1-216, NSF GOALI CMI-0700807/0700204, NSF CMMI-1101007 and a Grant from SINTEF. John Evans was partially supported by a DOE Computational Science Graduate Fellowship provided under Grant DE-FG02-97ER25308, and Michael Scott was partially supported by an ICES CAM Graduate Fellowship.
- Adaptivity with NURBS
- Finite cell method
- Hierarchical refinement
- Immersed boundary analysis
- Isogeometric analysis
- T-spline CAD surfaces