基于环路更新的物理覆盖和接触环路生成算法

Algorithm for generation of physical cover and contact loops based on loop updating

数值流形方法(NMM)实现了对连续和非连续问题的统一求解,但前提是必须能够正确地生成物理覆盖和接触环路。首先,针对几何形态保持固定不变的模型,阐述了物理覆盖和接触环路生成的整个过程。其中,重点介绍了搜索环路的算法,这也是NMM前处理的核心算法。进而,基于更新物理片环路和接触环路的思想,提出了一种新颖的更贴近NMM本质的裂纹扩展时的物理覆盖和接触环路生成算法,理论上可适用于任意的裂纹扩展长度和允许裂纹尖端落在单元的任意位置,更大程度上摆脱了对于网格的依赖性。最后,通过一个多裂纹扩展算例证实了方法的鲁棒性和正确性。

The numerical manifold method has been successful in solving continuous and discontinuous problems in a unified way, but the precondition is to generate the physical cover and contact loops correctly. For problem domains invariant during analysis, at first, the generation process of the physical cover and contact loops is expounded, where an algorithm for searching for loops, as the core of NMM pre-processing, is emphasized. Furthermore, a new algorithm much closer to the nature of NMM for the generation of physical cover and contact loops during the crack growth is proposed based on the concept of updating physical patch loops and contact loops. In theory, it is suitable for the cases of arbitrary crack growth length, and the crack tips are allowed to stop at any point of the manifold element, which has eliminated the mesh dependence to a great degree. Finally, the robustness and correctness of the proposed method is confirmed by an example of multiple crack growth.