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| 小变形结构接触问题的切割有限元法 |
| Cut Finite Element Method for Small Deformable Structural Contact Problems |
| 投稿时间：2025-11-07 修订日期：2025-12-08 |
| DOI： |
| 中文关键词: 接触力学 切割有限元法 小变形 小滑移 增广拉格朗日法 |
| 英文关键词:Contact Mechanics Cut Finite Element Method Small Deformation Small Sliding Augmented Lagrange Method |
| 基金项目:国家自然科学基金项目青年基金 |
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| 摘要点击次数: 139 |
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| 中文摘要: |
| 本文提出了一种基于切割有限元法与增广拉格朗日法相结合的小变形结构接触问题数值模拟框架。该方法通过将几何边界与背景网格解耦，实现了对非匹配网格和小滑移问题的高效处理。文中构建了统一的接触对抽象模型，设计了基于空间背景网格的快速接触搜索与精确投影算法，并通过若干数值实验验证了方法的准确性、收敛性和鲁棒性。本文方法为复杂接触问题的模拟提供了灵活可靠的数值工具。 |
| 英文摘要: |
| This paper proposes a numerical framework for simulating small-deformation structural contact problems by combining the Cut Finite Element Method (CutFEM) with the Augmented Lagrange Method (ALM). The method decouples the geometric boundaries from the background mesh, allowing effective treatment of non-matching meshes and small-sliding scenarios. A unified abstract contact-pair model is constructed, and efficient contact search and precise projection algorithms based on the spatial background mesh are designed. Several numerical experiments verify the accuracy, convergence, and robustness of the approach. The proposed method can serve as a flexible and reliable numerical tool for simulating complex contact phenomena. |
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