An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces

• DOI: 10.1016/j.cma.2012.03.017
• Publication Date: 2012-03-29T11:37:11Z
• Authors: Dominik Schillinger; Luca Dedè; Michael A. Scott; John A. Evans; Michael J. Borden; Ernst Rank; Thomas J.R. Hughes
• Keywords: T-spline CAD surfaces; Immersed boundary analysis; Isogeometric Analysis; Finite cell method; Adaptivity with NURBS; Finite cell method; Hierarchical refinement; Immersed boundary analysis; Isogeometric analysis; T-spline CAD surfaces; Computer Science Applications1707 Computer Vision and Pattern Recognition; Computational Mechanics; Mechanics of Materials; Mechanical Engineering; Physics and Astronomy (all); Adaptivity with NURBS; 0211 other engineering and technologies; 02 engineering and technology; Hierarchical refinement

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.