Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme

Extended finite element method (XFEM) is based on the idea of unit decomposition. The jump function that can reflect the discontinuity of the crack surface and the progressive displacement field function of the crack tip is added to the conventional finite element displacement mode, which avoids the...

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Main Author: GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng
Format: Article
Language:zho
Published: Editorial Office of Journal of Shanghai Jiao Tong University 2021-06-01
Series:Shanghai Jiaotong Daxue xuebao
Subjects:
Online Access:http://xuebao.sjtu.edu.cn/article/2021/1006-2467/1006-2467-55-6-689.shtml
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author GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng
author_facet GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng
author_sort GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng
collection DOAJ
description Extended finite element method (XFEM) is based on the idea of unit decomposition. The jump function that can reflect the discontinuity of the crack surface and the progressive displacement field function of the crack tip is added to the conventional finite element displacement mode, which avoids the inconvenience of remeshing the crack tip and the heavy calculation. Then the conventional finite element method calculates the fracture problem, and the crack propagation is independent of the mesh. When the standard finite element deals with time integration, the degree of freedom of the overall stiffness matrix will continue to increase in the process of crack propagation, which makes iterative calculation impossible. This paper proposes a novel Newmark implicit time integration scheme based on the XFEM to simulate dynamic crack growth. This method enriches all the nodes with the Heaviside function and the asymptotic displacement field function at the crack tip, that is, each node has 12 degrees of freedom, so that the overall stiffness matrix is consistent without making iterative calculation impossible. At the same time, a sparse matrix technology is proposed to solve the problems of large memory and long calculation time occupied by the matrix.
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spelling doaj.art-0f4a2b613c1e41fd8a2e7cf89f07703d2022-12-21T21:45:57ZzhoEditorial Office of Journal of Shanghai Jiao Tong UniversityShanghai Jiaotong Daxue xuebao1006-24672021-06-0155668969710.16183/j.cnki.jsjtu.2020.021Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration SchemeGUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng01. Xuzhen Railway Co., Ltd., Zhaotong 657900, Yunnan, China;2. School of Civil Engineering, Wuhan University, Wuhan 430072, China;3. Chongqing City Construction Investment (Group) Co., Ltd., Chongqing 400023, China;4. Department of Civil Engineering, Chongqing University, Chongqing 400045, ChinaExtended finite element method (XFEM) is based on the idea of unit decomposition. The jump function that can reflect the discontinuity of the crack surface and the progressive displacement field function of the crack tip is added to the conventional finite element displacement mode, which avoids the inconvenience of remeshing the crack tip and the heavy calculation. Then the conventional finite element method calculates the fracture problem, and the crack propagation is independent of the mesh. When the standard finite element deals with time integration, the degree of freedom of the overall stiffness matrix will continue to increase in the process of crack propagation, which makes iterative calculation impossible. This paper proposes a novel Newmark implicit time integration scheme based on the XFEM to simulate dynamic crack growth. This method enriches all the nodes with the Heaviside function and the asymptotic displacement field function at the crack tip, that is, each node has 12 degrees of freedom, so that the overall stiffness matrix is consistent without making iterative calculation impossible. At the same time, a sparse matrix technology is proposed to solve the problems of large memory and long calculation time occupied by the matrix.http://xuebao.sjtu.edu.cn/article/2021/1006-2467/1006-2467-55-6-689.shtmlextended finite element method (xfem)dynamic cracksnewmark implicit time integration schemesparse matrix technique
spellingShingle GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng
Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
Shanghai Jiaotong Daxue xuebao
extended finite element method (xfem)
dynamic cracks
newmark implicit time integration scheme
sparse matrix technique
title Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
title_full Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
title_fullStr Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
title_full_unstemmed Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
title_short Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme
title_sort numerical calculation method for crack dynamic propagation based on newmark implicit time integration scheme
topic extended finite element method (xfem)
dynamic cracks
newmark implicit time integration scheme
sparse matrix technique
url http://xuebao.sjtu.edu.cn/article/2021/1006-2467/1006-2467-55-6-689.shtml
work_keys_str_mv AT guodepinglizhengpengsenlinzengzhikaiwudaifeng numericalcalculationmethodforcrackdynamicpropagationbasedonnewmarkimplicittimeintegrationscheme