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三维裂纹扩展的自适应虚拟节点法
Adaptive Phantom Node Method for Three-dimensional Crack Propagation
投稿时间:2023-07-08  修订日期:2023-09-11
DOI:
中文关键词:  裂纹扩展  自适应网格加密  虚拟节点法  扩展有限元法  三维裂纹
英文关键词:crack propagation  adaptive mesh refinement  phantom node method  extended finite element method  three-dimensional cracks
基金项目:科学挑战专题(TZ2018002),中央高校基本科研业务费专项资金(DUT18LK04),国家自然科学基金面上项目(11672062)资助
作者单位邮编
冯泽洋 大连理工大学 116024
段庆林* 大连理工大学 116024
陈嵩涛 大连理工大学 
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中文摘要:
      本文在有限元方法的框架下针对三维裂纹扩展问题发展了自适应虚拟节点法。该方法采用无需裂尖加强函数(和相应的额外自由度)的虚拟节点技术描述裂纹处的间断,并采用单元局部水平集方法对三维裂纹面进行几何描述和追踪。为加速计算,提出了随裂纹面扩展的自适应网格加密方法。局部细化网格产生的悬空节点由简便的约束近似技术处理,无需引入额外自由度或特殊单元。所发展的自适应虚拟节点法便于数值实现,具有与标准有限元方法相当的鲁棒性。数值结果表明,该方法可有效模拟三维裂纹扩展过程,且能方便地应用于复杂工程结构的多裂纹扩展问题。
英文摘要:
      In this paper, an adaptive phantom node method is developed in the framework of the finite element method (FEM), aiming at three-dimensional crack propagation. The proposed method describes the discontinuity at cracks by the technique of phantom nodes, and the crack tip enrichment functions (and the corresponding extra degrees of freedom) are not needed. The geometrical description and tracking of the extending three-dimensional crack surfaces are treated by the element-local level set method. To accelerate the computation, adaptive mesh refinement along with crack surface extension is proposed. The hanging nodes which present in the locally refined mesh is treated by the simple technique of constrained approximation, and no extra degrees of freedom or special elements are involved. Numerical implementation of the presented adaptive phantom node method is convenient and its robustness is comparable to the standard FEM. Numerical results show that the proposed method is able to simulate three-dimensional crack propagation and it can be conveniently applied to model multiple cracks extending in complex engineering structures.
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