上海交通大学学报 ›› 2021, Vol. 55 ›› Issue (6): 689-697.doi: 10.16183/j.cnki.jsjtu.2020.021
所属专题: 《上海交通大学学报》2021年“土木建筑工程”专题; 《上海交通大学学报》2021年12期专题汇总专辑
郭德平1,2, 李铮3(), 彭森林4, 曾志凯3, 吴岱峰3
收稿日期:
2020-01-14
出版日期:
2021-06-28
发布日期:
2021-06-30
通讯作者:
李铮
E-mail:2756232300@qq.com
作者简介:
郭德平(1983-),男,高级工程师,主要从事隧道工程和岩土工程等方面的科研工作
基金资助:
GUO Deping1,2, LI Zheng3(), PENG Senlin4, ZENG Zhikai3, WU Daifeng3
Received:
2020-01-14
Online:
2021-06-28
Published:
2021-06-30
Contact:
LI Zheng
E-mail:2756232300@qq.com
摘要:
扩展有限单元法(XFEM)是基于单位分解的思想,在常规有限元的位移模式中加入能够反映裂纹面不连续性的跳跃函数和裂纹尖端的渐近位移场函数,避免了常规有限单元法计算断裂问题时需要对裂纹尖端重新划分网格的不便以及繁重的计算量,并且裂纹的扩展独立于网格.标准有限元在处理时间积分时,在裂纹不断扩展的过程中整体刚度矩阵的自由度也会不断地增大,从而导致迭代计算无法进行.本文基于扩展有限单元法模拟动态裂纹扩展的方法,提出了新的Newmark隐式时间积分方案.此方法将所有节点都富集Heaviside函数和裂纹尖端的渐近位移场函数,即每个节点都有12个自由度,从而使得总体刚度矩阵式保持一致,避免迭代计算无法进行.同时,提出了一种稀疏矩阵技术来解决矩阵所占内存大和计算时间长的问题.
中图分类号:
郭德平, 李铮, 彭森林, 曾志凯, 吴岱峰. 基于Newmark隐式时间积分方案的裂纹动态扩展的数值计算方法[J]. 上海交通大学学报, 2021, 55(6): 689-697.
GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng. Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme[J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 689-697.
[1] |
SHEN J H, WHEELER C, ILIC D, et al. Application of open source FEM and DEM simulations for dynamic belt deflection modelling[J]. Powder Technology, 2019, 357:171-185.
doi: 10.1016/j.powtec.2019.08.068 URL |
[2] |
ELGUEDJ T, JAN Y, COMBESCURE A, et al. X-FEM Analysis of dynamic crack growth under transient loading in thick shells[J]. International Journal of Impact Engineering, 2018, 122:228-250.
doi: 10.1016/j.ijimpeng.2018.08.013 URL |
[3] |
SHARMA V, FUJISAWA K, MURAKAMI A. Space-time FEM with block-iterative algorithm for nonlinear dynamic fracture analysis of concrete gravity dam[J]. Soil Dynamics and Earthquake Engineering, 2020, 131:105995.
doi: 10.1016/j.soildyn.2019.105995 URL |
[4] |
SUN J S, LEE K H, LEE H P. Comparison of implicit and explicit finite element methods for dynamic problems[J]. Journal of Materials Processing Technology, 2000, 105(1/2):110-118.
doi: 10.1016/S0924-0136(00)00580-X URL |
[5] | NILSSON K, LIDSTRÖM P. Simulation of ductile fracture of slabs subjected to dynamic loading using cohesive elements[J]. International Journal of Da-mage Mechanics, 2012, 21(6):871-892. |
[6] |
BELYTSCHKO T, BLACK T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 45(5):601-620.
doi: 10.1002/(ISSN)1097-0207 URL |
[7] |
ZHOU X P, ZHANG J Z, BERTO F. Fracture ana-lysis in brittle sandstone by digital imaging and AE techniques: Role of flaw length ratio[J]. Journal of Materials in Civil Engineering, 2020, 32(5):04020085.
doi: 10.1061/(ASCE)MT.1943-5533.0003151 URL |
[8] |
ZHOU X P, CHENG H. Multidimensional space method for geometrically nonlinear problems under total Lagrangian formulation based on the extended finite-element method[J]. Journal of Engineering Mechanics, 2017, 143(7):04017036.
doi: 10.1061/(ASCE)EM.1943-7889.0001241 URL |
[9] |
CHEN J W, ZHOU X P. The enhanced extended finite element method for the propagation of complex branched cracks[J]. Engineering Analysis With Boundary Elements, 2019, 104:46-62.
doi: 10.1016/j.enganabound.2019.03.028 URL |
[10] |
STOLARSKA M, CHOPP D L, MOËS N, et al. Modelling crack growth by level sets in the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2001, 51(8):943-960.
doi: 10.1002/nme.201 URL |
[11] |
ZHOU X P, CHEN J W. Extended finite element simulation of step-path brittle failure in rock slopes with non-persistent en-echelon joints[J]. Engineering Geology, 2019, 250:65-88.
doi: 10.1016/j.enggeo.2019.01.012 URL |
[12] | CHEN J W, ZHOU X P, BERTO F. The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method[J]. Fatigue & Fracture of Engineering Materials & Structures, 2019, 42(2):397-414. |
[13] | 黄宏伟, 刘德军, 薛亚东, 等. 基于扩展有限元的隧道衬砌裂缝开裂数值分析[J]. 岩土工程学报, 2013, 35(2):266-275. |
HUANG Hongwei, LIU Dejun, XUE Yadong, et al. Numerical analysis of cracking of tunnel linings based on extended finite element[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(2):266-275. | |
[14] | 阮滨, 陈国兴, 王志华. 基于扩展有限元法的均质土坝裂纹模拟[J]. 岩土工程学报, 2013, 35(Sup.2):49-54. |
RUAN Bin, CHEN Guoxing, WANG Zhihua. Numerical simulation of cracks of homogeneous earth dams using an extended finite element method[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(Sup.2):49-54. | |
[15] |
MENOUILLARD T, BELYTSCHKO T. Dynamic fracture with meshfree enriched XFEM[J]. Acta Mechanica, 2010, 213(1/2):53-69.
doi: 10.1007/s00707-009-0275-z URL |
[16] | WEN L F, TIAN R. Improved XFEM: Accurate and robust dynamic crack growth simulation[J]. Compu-ter Methods in Applied Mechanics and Engineering, 2016, 308:256-285. |
[17] |
ZHOU X P, ZHANG J Z, QIAN Q H, et al. Expe-rimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and AE techniques[J]. Journal of Structural Geology, 2019, 126:129-145.
doi: 10.1016/j.jsg.2019.06.003 URL |
[18] |
WANG Y T, ZHOU X P, XU X. Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics[J]. Engineering Fracture Mechanics, 2016, 163:248-273.
doi: 10.1016/j.engfracmech.2016.06.013 URL |
[19] |
WU Z J, FAN L F, LIU Q S, et al. Micro-mechanical modeling of the macro-mechanical response and fracture behavior of rock using the numerical manifold method[J]. Engineering Geology, 2017, 225:49-60.
doi: 10.1016/j.enggeo.2016.08.018 URL |
[20] |
CHEN S, HANSEN J M, TORTORELLI D A. Unconditionally energy stable implicit time integration: Application to multibody system analysis and design[J]. International Journal for Numerical Methods in Engineering, 2000, 48(6):791-822.
doi: 10.1002/(ISSN)1097-0207 URL |
[21] |
WANG J R, WU J C, WANG D D. A quasi-consis-tent integration method for efficient meshfree analysis of Helmholtz problems with plane wave basis functions[J]. Engineering Analysis With Boundary Elements, 2020, 110:42-55.
doi: 10.1016/j.enganabound.2019.10.002 URL |
[22] |
WANG D D, WU J C. An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 349:628-672.
doi: 10.1016/j.cma.2019.02.029 URL |
[23] |
WANG D D, WANG J R, WU J C, et al. A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations[J]. Frontiers of Structural and Civil Engineering, 2019, 13(2):337-352.
doi: 10.1007/s11709-018-0467-5 URL |
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