| 罗飞,郭玉杰,孙芳斌,张兴.基于Bézier三角形的曲面网格划分及等几何板壳分析[J].计算力学学报,2025,42(5):825~830,838 |
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| 基于Bézier三角形的曲面网格划分及等几何板壳分析 |
| Bézier triangular surface mesh generation and isogeometric plate and shell analysis |
| 投稿时间：2023-11-18 修订日期：2024-02-07 |
| DOI：10.7511/jslx20231118001 |
| 中文关键词: 等几何分析 Bézier三角网格划分 Bézier曲面映射 曲线裁剪 Kirchhoff-love壳 |
| 英文关键词:isogeometric analysis Bézier triangular mesh Bézier surface mapping Curves trim Kirchhoff-love shell |
| 基金项目:国家自然科学基金面上项目(11972187);中央高校基本科研业务费(NT2022004)资助项目. |
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| 中文摘要: |
| 针对单张NURBS曲面提出了一套考虑裁剪与非裁剪形式的Bézier三角形网格划分方法,并将其应用于等几何Kirchhoff-Love壳结构的分析中。首先,将NURBS曲面插值为Bézier曲面;其次,在参数域内计算裁剪曲线与各个参数节点的拓扑关系,并在裁剪曲线上取点,生成参数域内的Bézier轮廓曲线集合;基于该轮廓曲线集合,生成参数域上的三角形网格;最后,采用映射法生成物理域上的Bézier三角网格。通过三个模型验证了算法的适应性与鲁棒性,并计算了网格质量,结果表明整体网格质量良好;在此基础上,以Scordelis-Lo's Roof壳模型为例,采用罚函数法施加Kirchhoff-Love壳单元间的转动约束,验证了基于Bézier三角形的Kirchhoff-Love壳单元的精度。 |
| 英文摘要: |
| This paper presents a Bezier triangle meshing method that considers both clipped and non-clipped forms for a single NURBS surface.The proposed method is applied to analyze isogeometric Kirchhoff-Love shell structures.The process begins by interpolating NURBS surfaces into Bezier surfaces.Subsequently,the topological relationship between the clipping curve and each parameter node is calculated within the parameter domain.A Bezier contour curve set is then generated in the parameter domain by selecting points along the clipping curve.Utilizing this contour curve set,a triangular mesh is generated in the parameter domain.Finally,the Bezier triangle mesh in the physical domain is created through a mapping method.The adaptability and robustness of the algorithm are verified through three models,and the mesh quality is assessed.The results demonstrate favorable overall mesh quality.Building upon this foundation,the paper illustrates the application of a rotation constraint between Kirchhoff-Love shell elements,using the penalty function method with Scordelis-Lo's Roof shell model as an example.The accuracy of Kirchhoff-Love shell elements based on Bezier triangles is subsequently validated. |
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