用于连续体与非连续体共存转化计算的质点元方法
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摘要
为了进行建筑结构倒塌全过程的力学模拟,针对建筑结构倒塌数值模拟梁壳单元几何、材料、接触三重非线性且连续体向非连续体转化的动力计算问题,提出了显式有限元与离散元的统一模型"质点元方法",该方法通过定义广义连接模型、构造连接模型转化法则和建立接触碰撞算法,将显式有限元与离散元统一于相同的计算框架之下,较好地继承了有限元的单元技术、本构技术以及离散元的非连续体计算能力,具有效率优先、精度可调的特点。通过某框架剪力墙结构计算表明,质点元方法能够用于建筑结构倒塌的连续体与非连续体共存及转化的强非线性动力计算。
In order to simulate the nonlinear dynamic process of building structure collapse,considering the coupled nonlinearity of geometrical,material and contact from continuum to non-continuum,a particle element method(PEM) was proposed to simulate the nonlinear dynamic process of building structure collapse.The PEM,which inherits the element and material techniques of the finite element method and non-continuum computational power of discrete element method,unifies the explicit finite element method(EFEM) and discrete element method(DEM) to the same computation framework by defining the generalized link model,constructing the conversion law of the link model and the contact collision algorithm.The PEM,which gives priority to efficiency while precision can be adjusted,can be used for strong nonlinear dynamic simulation of building structure collapse that continuum and non-continuum both exist.
In order to simulate the nonlinear dynamic process of building structure collapse,considering the coupled nonlinearity of geometrical,material and contact from continuum to non-continuum,a particle element method(PEM) was proposed to simulate the nonlinear dynamic process of building structure collapse.The PEM,which inherits the element and material techniques of the finite element method and non-continuum computational power of discrete element method,unifies the explicit finite element method(EFEM) and discrete element method(DEM) to the same computation framework by defining the generalized link model,constructing the conversion law of the link model and the contact collision algorithm.The PEM,which gives priority to efficiency while precision can be adjusted,can be used for strong nonlinear dynamic simulation of building structure collapse that continuum and non-continuum both exist.
引文
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[15]Ted Belytschko,Neal M O.Contact-impact by thepinball algorithm with penalty and Lagrangian methods[J].International Journal for Numerical Methods inEngineering,1991,131:547-572.
[2]Robert D Cook,David S Malkus,Michael E Plesha,et al.Concepts and applications of fimite elementanalysis[M].Evanston,Illinois:John Wiley&Sons,2001.
[3]Hallquist J O.LS-DYNA theory Manual[M].Livermore Software Technology Corporation,2006.
[4]魏群.散体单元法的基本原理数值方法及程序[M].北京:科学出版社,1991.(Wei Qun.The basicprinciples of discrete element method,numerical methodand program[M].Beijing:Science Press,1991.(inChinese))
[5]万福磊,李云贵.建筑结构连续性倒塌力学特点与数值模拟方法[C]//第十五届全国工程设计计算机应用学术会议论文集.哈尔滨:哈尔滨工业大学出版社,2010:13-18.(Wan Fulei,Li Yungui.Numericalsimulation method and charactors of building structureprogressive collapse[C]//The 15th EngineeringDesign and Computer Technique ConferenceProceedings.Harbin:Harbin Institute of TechnologyPress,2010:13-18.(in Chinese))
[6]方韬,龚顺风,金伟良.混凝土结构破坏过程的离散单元法模拟[J].浙江大学学报:工学版,2004,38(7):921-925.(Fang Tao,Gong Shunfeng,JINWeiliang.Failure process simulation of concretestructures by discrete element method[J].Journal ofZhejiang University:Engineering Science,2004,38(7):921-925.(in Chinese))
[7]成名,刘维甫,刘凯欣.高速冲击问题的离散元法数值模拟[J].计算力学学报,2009,26(4):591-594.(Cheng Ming,Liu Weifu,Liu Kaixin.Numericalsimulation for high-speed impact problems by discreteelement method[J].Chinese Journal of ComputationalMechanics,2009,26(4):591-594.(in Chinese))
[8]万福磊.建筑结构连续性倒塌数值模拟方法研究[D].北京:中国建筑科学研究院,2011:45-63.(WanFulei.Research on the numerical simulation method ofbuilding structure progressive collapse[D].Beijing:China Academy of Building Research,2011:45-63.(in Chinese))
[9]Ted Belytschko,Wing Kam Liu,Brian Moran.Nonlinear finite elements for continua and structures[M].Evanston,Illinois:John Wiley&Sons Ltd.,2000.
[10]Ted Belytschko,Schwer L.Large displacementtransient analysis of space frames[J].InternationalJournal for Numerical Methods in Engineering,1977,11:65-84.
[11]Ted Belytschko,Lin J,Tsay C S.Explicit algorithmsfor the nonlinear dynamics of shells[J].ComputerMethods in Applied Mechanics and Engineering,1984,42:225-251.
[12]胡晓斌,钱稼茹.结构连续倒塌分析与设计方法概述[J].建筑结构,2006,36(增刊):79-83.(Hu Xiaobin,Qian Jiaru.Overview of analysis and design approachesfor progressive collapse of structures[J].BuildingStructure,2006,36(Suppl.):79-83.(in Chinese))
[13]李伟,朱德懋.不连续散粒体的离散单元法[J].南京航空航天大学学报,1999,31(1):85-91.(Li Wei,Zhu Demao.Discrete element method of discontinuousgranular media[J].Journal of Nanjing University ofAeronautics&Astronautics,1999,31(1):85-91.(inChinese))
[14]王福军.冲击接触问题有限元法并行计算及其工程应用[D].北京:清华大学,2000:45-80.(WangFujun.Parallel computation of contact-impact problemswith FEM and its engineering application[D].Beijing:Tsinghua University,2000:45-80.(in Chinese))
[15]Ted Belytschko,Neal M O.Contact-impact by thepinball algorithm with penalty and Lagrangian methods[J].International Journal for Numerical Methods inEngineering,1991,131:547-572.
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