Isogeometric analysis for trimmed CAD surfaces
Isogeometric analysis for trimmed CAD surfaces
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DOI：
10.1016/j.cma.2009.05.004
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发表时间：
2009-08
影响因子：
7.2
通讯作者：
Hyun-Jung Kim;Yu-Deok Seo;S. Youn
中科院分区：
文献类型：
--
作者：
Hyun-Jung Kim;Yu-Deok Seo;S. Youn
在这项工作中，提出了二维线弹性问题中修剪 CAD 曲面的等几何分析。该方法的主要优点是不需要额外的模型来分析修剪的表面。作为等几何分析中修剪曲面处理的开创性尝试，直接利用CAD系统导出的修剪曲线和修剪曲面信息进行分析。为此，通过使用投影方案来搜索修剪的元素。对于修剪单元的集成，采用 NEFEM 中采用的 NURBS 增强集成方案。对于等几何分析，提出了基于样条基函数的刚度矩阵的构造。在公式中，修整曲线上的信息不仅用于获取积分点，还用于计算雅可比行列式。通过对验证算例的误差分析，考察了所提方法的鲁棒性和有效性。据观察，所提出的方法给出了理论收敛速度。使用所提出的方法可以轻松处理传统等几何分析难以分析的多修剪曲线问题。给出了一个很有启发性的例子。在同一示例中，还采用了 T 样条局部细化。
In this work, an Isogeometric analysis for trimmed CAD surfaces in 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional modeling for the analysis of the trimmed surface is necessary. As a pioneering attempt to deal with the trimmed surfaces in Isogeometric analysis, the information on the trimming curves and trimmed surfaces exported from CAD system is directly utilized for analysis. For this, trimmed elements are searched through using a projection scheme. For the integration of trimmed elements, NURBS-enhanced integration scheme employed in NEFEM is adopted. For the Isogeometric analysis, the construction of the stiffness matrix based on the spline basis function is presented. In the formulation, the information on the trimming curves is used not only for obtaining integration points but also for calculating the Jacobian. Through error analyses of the verification examples, the robustness and effectiveness of the proposed method are investigated. It is observed that the proposed method gives the theoretical convergence rate. Multiple-trimming-curve problems which are difficult to analyze with conventional Isogeometric analysis are easily treated with the proposed method. An illuminating example is given. In the same example, T-spline local refinement is also employed.