A robust algorithm for the generation of integration cells in Numerical Manifold Method

被引:10
作者
Cai, Yongchang [1 ,2 ]
Wu, Jie [1 ,2 ]
机构
[1] Tongji Univ, State Key Lab Disaster Reduct Civil Engn, Shanghai 200092, Peoples R China
[2] Tongji Univ, Dept Geotech Engn, Shanghai 200092, Peoples R China
基金
中国国家自然科学基金;
关键词
NMM; Finite cover system; Cracks; Integration cell; Tessellation approach; FINITE-ELEMENT-METHOD; ADAPTIVE MULTISCALE METHOD; PHANTOM-NODE METHOD; CRACK-PROPAGATION; DYNAMIC CRACK; FRACTURE; PARTITION; SIMULATION; MODELS; GROWTH;
D O I
10.1016/j.ijimpeng.2015.10.015
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
The finite cover system plays a critical role in Numerical Manifold Method (NMM) for the unified simulation of models from continuum to discontinuum. However, large amounts of computational geometries are usually involved in the traditional finite cover generation algorithm, which makes the process of finite cover generation a time consuming and error prone task and limits the wide applications of NMM. To achieve a simple and robust finite cover generation algorithm for NMM, a new method for the generation of integration cells including closed convex or concave polygons was developed in this paper as an important supplement to our recent work [Cai et al., 2013]. In the newly developed integration cells generation algorithm, with the help of pre-defined symbol functions and 3 different matrixes, nodes including vertexes and intersection points belonging to a same integration cell were first grouped together, and then listed in a anticlockwise manner to finally form the closed circuit. In this way, large amounts of computational geometries employed in the identification of integration cells were replaced with computational algebras. Several benchmarks were simulated to investigate the accuracy of the proposed integration cells generation algorithm and to demonstrate the robustness of NMM. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码:165 / 176
页数:12
相关论文
共 39 条
[1]  
[Anonymous], 2005, FRACTURE MECH FUNDAM
[2]  
Babuska I, 1997, INT J NUMER METH ENG, V40, P727, DOI 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO
[3]  
2-N
[4]   A spline-based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations [J].
Benowitz, Brett A. ;
Waisman, Haim .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2013, 95 (05) :361-386
[5]   An adaptive multiscale method for quasi-static crack growth [J].
Budarapu, Pattabhi R. ;
Gracie, Robert ;
Bordas, Stephane P. A. ;
Rabczuk, Timon .
COMPUTATIONAL MECHANICS, 2014, 53 (06) :1129-1148
[6]   Efficient coarse graining in multiscale modeling of fracture [J].
Budarapu, Pattabhi R. ;
Gracie, Robert ;
Yang, Shih-Wei ;
Zhuang, Xiaoying ;
Rabczuk, Timon .
THEORETICAL AND APPLIED FRACTURE MECHANICS, 2014, 69 :126-143
[7]  
Cai YC, 2013, CMES-COMP MODEL ENG, V92, P63
[8]   A GENERALIZED AND EFFICIENT METHOD FOR FINITE COVER GENERATION IN THE NUMERICAL MANIFOLD METHOD [J].
Cai, Yongchang ;
Zhuang, Xiaoying ;
Zhu, Hehua .
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2013, 10 (05)
[9]   A new partition of unity finite element free from the linear dependence problem and possessing the delta property [J].
Cai, Yongchang ;
Zhuang, Xiaoying ;
Augarde, Charles .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (17-20) :1036-1043
[10]   Phantom-node method for shell models with arbitrary cracks [J].
Chau-Dinh, Thanh ;
Zi, Goangseup ;
Lee, Phill-Seung ;
Rabczuk, Timon ;
Song, Jeong-Hoon .
COMPUTERS & STRUCTURES, 2012, 92-93 :242-256