岩石冲击破坏的数值流形方法模拟(英文)
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摘要
岩石冲击破坏是一种典型的动力学问题。为了更好地利用数值流形方法对动力学问题进行分析,本文在对原数值流形方法中的动力学问题求解思想进行分析的基础上,采用动力有限元方法中的Newmark法对该算法进行了改进。改进后的数值流形方法与原来相比具有3个明显的优势:①当选择合适的参数后,该方法能够保证解的无条件收敛;②可以采用比原算法大的多的时间步长;③充分地考虑了动力学问题中的阻尼效应。最后通过一个算例说明了改进后的数值流形方法能够很好地模拟岩石在冲击载荷作用下破坏的全过程,克服了有限元法不能模拟岩石破坏后块体运动情况的不足。
Impact failure of rock is a kind of typical dynamic problem.In order to perfectly analyze the dynamic problem by use of numerical manifold method(NMM),the Newmark method of dynamic finite element method was adopted to improve the algorithm in original NMM on the basis of analyzing the solution idea of dynamics problem in NMM.There were three obvious advantages in the improved method over the original one: ①The solution of this method was convergent without any condition when suitable parameters were selected;②The time step adopted in this method was much longer than that in the original one;③The damping effect in the dynamic problem was fully considered.In the end,a calculation example was used to illustrate the application of this method in simulation of the whole process of impact failure of rock,which overcame the shortcomings of FEM in simulating the block movement after rock failure.
Impact failure of rock is a kind of typical dynamic problem.In order to perfectly analyze the dynamic problem by use of numerical manifold method(NMM),the Newmark method of dynamic finite element method was adopted to improve the algorithm in original NMM on the basis of analyzing the solution idea of dynamics problem in NMM.There were three obvious advantages in the improved method over the original one: ①The solution of this method was convergent without any condition when suitable parameters were selected;②The time step adopted in this method was much longer than that in the original one;③The damping effect in the dynamic problem was fully considered.In the end,a calculation example was used to illustrate the application of this method in simulation of the whole process of impact failure of rock,which overcame the shortcomings of FEM in simulating the block movement after rock failure.
引文
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[2]石根华.数值流形方法与非连续变形分析[M].裴觉民,译.北京:清华大学出版社,1997.(SHI Gen-hua.Numerical manifold method and discontinuous analysis[M].PEI Jue-min,translator.Beijing:Tsinghua University Press,1997.(in Chinese))
[3]CHIOU Yaw-jeng,LEE Yu-min,TSAY Ren-jow.Mixed mode fracture propagation by manifold method[J].International Journal of Fracture,2002,114:327–347.
[4]范天佑.断裂理论基础[M].北京:科学出版社,2003.(FANTian-you.Foundation of fracture theory[M].Beijing:Science Press,2003.(in Chinese))
[5]类维生,董建令,姚枚.动态断裂过程的惯性效应[J].理化检验-物理分册,1996,32(4):32–34.(LEI Wei-sheng,DONG Jian-ling,YAO Mei.Inertial effect in dynamics fracture[J].Physics and Chemistry Test-physics Fascicule,1996,32(4):32–34.(in Chinese))
[6]彭自强.数值流形方法与裂纹动态扩展模拟[D].武汉:中国科学院武汉岩土力学研究所,2003:57–61.(PENG Zhi-qiang.Numerical manifold method and simulation of crack dynamic propagation[D].Wuhan:Wuhan Institute of Rock and Soil Mechanics of Chinese Academy of Sciences,2003:57–61.(in Chinese))
[7]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1995.(WANG Xu-cheng,SHAO Min.Basic principle and numerical method of finite element method[M].Beijing:Tsinghua University Press,1995.(inChinese))
[8]张国新,彭静.二阶流形元与结构变形分析[J].力学学报,2002,34(2):261–269.(ZHANG Guo-xin,PENG Jing.Second-order manifold method in structure failure analysis[J].Acta Mechanica Sinica,2002,34(2):261–269.(in Chinese))
[9]唐友刚.高等结构动力学[M].天津:天津大学出版社,2002.(TANG You-gang.Advanced structural dynamics[M].Tianjin:Tianjin University Press,2002.(in Chinese))
[10]高尔新,杨仁树.爆破工程[M].北京:中国矿业大学出版社,1999.(GAO Er-xin,YANG Ren-shu.Blasting engineering[M].Beijing:China University of Science & Technology Press,1999.(in Chinese))
[11]刘再华,解德,王元汉,等.工程断裂动力学[M].武汉:华中理工大学出版社,1996.(LIU Zai-hua,XIE De,WANG Yuan-han,et al.Engineering fracture dynamics[M].Wuhan:Huazhong University of Science&Technology Press,1996.(in Chinese))
[12]张国新,金锋,王光伦.用基于流形元的子域奇异边界元法模拟重力坝的地震破坏[J].工程力学,2001,18(4):18–27.(ZHANG Guo-xin,JIN Feng,WANG Guang-lun.Seismic failure simulation of gravity dam by manifold-based singular boundary element method[J].Engineering Mechanics,2001,18(4):18–27.(in Chinese))
[13]张国新,王光伦,裴觉民.基于流形元法的结构破坏分析[J].岩石力学与工程学报,2001,20(3):281–287.(ZHANG Guo-xin,WANG Guang-lun,PEI Jue-min.Structure failure analysis based on manifold method[J].Chinese Journal of Rock Mechanics and Rock Engineering,2001,20(3):281–287.(in Chinese))
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