An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
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DOI：
10.1016/j.cma.2012.03.017
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发表时间：
2012-12
影响因子：
7.2
通讯作者：
D. Schillinger;L. Dede’;M. Scott;John A. Evans;Michael J. Borden;E. Rank;T. Hughes
中科院分区：
文献类型：
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作者：
D. Schillinger;L. Dede’;M. Scott;John A. Evans;Michael J. Borden;E. Rank;T. Hughes
我们探索 NURBS 的层次细化作为自适应等几何和浸入边界分析的基础。我们使用 B 样条细分的原理来导出局部细化程序，该程序将基础的全面分析适用性与树数据结构中的直接实现和对更高维度的简单推广结合起来。我们针对一些二维和三维的基本流体和结构分析问题测试了 NURBS 的分层细化，并在所有情况下都取得了良好的结果。使用 B 样条版本的有限单元方法，我们展示了浸入边界方法作为无缝等几何设计到分析程序的潜力，适用于由 T 样条 CAD 曲面定义的复杂工程零件，特别是船舶螺旋桨和汽车车轮。我们表明，分层细化通过自适应解决局部特征，显着提高了该方法的灵活性。
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.