| 谢晴天,谢贤达,罗年猛,杨奥迪,王书亭.面向复杂CAD模型的嵌入域等几何单元几何属性快速界定方法[J].计算力学学报,2025,42(1):61~67 |
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| 面向复杂CAD模型的嵌入域等几何单元几何属性快速界定方法 |
| An efficient method determining cell geometric attribute of immersed isogeometric analysis for complex CAD models |
| 投稿时间：2023-09-11 修订日期：2023-10-14 |
| DOI：10.7511/jslx20230911002 |
| 中文关键词: CAD 等几何分析 嵌入域法 单元几何属性 分离轴理论 射线法 |
| 英文关键词:complex CAD models isogeometric analysis embedded domain method cell geometric attribute separation axis theory ray-tracing method |
| 基金项目:国家重点研发计划(2020YFB1708300);国家自然科学青年基金(52205267)资助项目. |
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| 中文摘要: |
| 嵌入域等几何分析方法可以综合嵌入域法网格划分和等几何分析高阶单元求解效率的双重优势,是复杂CAD模型进行等几何分析的主要实现方式之一。嵌入域网格单元几何属性的界定是构建嵌入域等几何分析模型的关键环节之一。针对基于射线法对嵌入域网格单元进行几何属性界定过程中存在的界定效率与准确度相矛盾的问题,本文将分离轴理论与射线法结合,建立了一种混合型网格单元几何属性界定策略,将点与体的相对位置关系判断问题转化为了面与体的相交判断问题,从而在保证单元几何属性界定效率的同时,提高单元界定准确度。数值算例表明,本文提出的混合型网格单元几何属性界定策略可有效提升界定效率及鲁棒性,为复杂模型嵌入域等几何分析奠定基础。 |
| 英文摘要: |
| As one of the main approaches to implementing isogeometric analysis(IGA) for complex CAD models,immersed isogeometric analysis integrates the advantage of the embedded domain method in mesh generation and the merit of IGA in solution efficiency for higher-order elements.Determining the cell’s geometric attributes is one of the key aspects in immersed isogeometric analysis method.In this paper,we combine the separation axis theory with the ray-tracing method to present a hybrid cell’s geometric attributes determining strategy,aiming at the contradiction between the efficiency and accuracy in the cell’s geometric attributes existing in the traditional ray-tracing method.The proposed method transforms the problem of the relative position relationship determination between points and solid into the intersection determination between solid and surfaces,which enables a faster and more accurate determination of the cell geometric attributes.The numerical examples show that the proposed hybrid strategy can effectively improve the efficiency and robustness of the determination,laying the foundation of immersed isogeometric analysis for complex models. |
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