Song Shi, Braun Moritz, Wiegard Bjarne, Herrnring Hauke, Ehlers Sören
Institute for Ship Structural Design and Analysis, Am Schwarzenberg Campus 4 c, Hamburg University of Technology, 21073 Hamburg, Germany.
Materials (Basel). 2021 Dec 29;15(1):240. doi: 10.3390/ma15010240.
H-adaptivity is an effective tool to introduce local mesh refinement in the FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures, such as ship hulls. Meanwhile, in engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks, such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called 'h-adaptive element splitting' (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that mostly consist of structured coarse meshes, which is also beneficial to the reduction of computational resources. By employing the h-AES method, very small cracks are well represented in large structures without any deletions of elements.
在基于有限元法的裂纹扩展数值模拟中，h 自适应是引入局部网格细化的有效工具。h 自适应的实现有利于涉及大型结构（如船体）的疲劳或偶然载荷场景的数值模拟。同时，在工程应用中，单元删除法经常用于表示裂纹。然而，单元删除法存在一些缺点，如强烈的网格依赖性以及质量或能量的损失。为了缓解这个问题，可以应用单元分裂法。在本研究中，引入了一种名为“h 自适应单元分裂”（h-AES）的数值方法。h-AES 方法通过将 h 自适应与单元分裂法相结合应用于有限元程序中。给出了两个使用 h-AES 方法在线弹性断裂力学场景下模拟大型结构裂纹的例子。数值结果与解析解进行了验证。基于这些例子，证明 h-AES 方法能够在主要由结构化粗网格组成的大规模数值模型中引入网格细化，这也有利于减少计算资源。通过采用 h-AES 方法，非常小的裂纹在大型结构中能得到很好的表示，而无需删除任何单元。
