一种用于建筑结构倒塌数值模拟的质点元方法
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摘要
针对建筑结构倒塌过程的梁壳单元几何、材料、接触三重非线性且连续介质向非连续介质转化的动力计算问题,提出了能够考虑多重非线性用于连续介质与非连续介质共同作用且动态转化计算的质点元方法。该方法以质点运动学为基础,建模过程与有限元一致,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,具备有限元连续介质阶段的计算精度和离散元非连续介质阶段的计算能力,能够用于建筑结构倒塌等强非线性的动力计算。
Considering the coupled nonlinearity of geometrical,material and contact,a particle element method(PEM) was proposed to simulate the nonlinear dynamics process of building structure collapse from continuum to noncontinuum.Based on the theory of particle dynamics,this method unifies the explicit finite element method and the discrete element method to the same computation framework by defining the generalized link modal,constructing the conversion law of the link modal and creating the contact collision algorithm.The particle element method,which has the computation accuracy of finite element method during the continuum phase and the computation capability of discrete element method during the noncontinuum phase,could be used for strong nonlinear dynamics simulation of building structure collapse.
Considering the coupled nonlinearity of geometrical,material and contact,a particle element method(PEM) was proposed to simulate the nonlinear dynamics process of building structure collapse from continuum to noncontinuum.Based on the theory of particle dynamics,this method unifies the explicit finite element method and the discrete element method to the same computation framework by defining the generalized link modal,constructing the conversion law of the link modal and creating the contact collision algorithm.The particle element method,which has the computation accuracy of finite element method during the continuum phase and the computation capability of discrete element method during the noncontinuum phase,could be used for strong nonlinear dynamics simulation of building structure collapse.
引文
[1]王福军,黎耀军,K.Han,Y.T.Feng.一种用于结构动态过程数值模拟的广义有限元法[J].中国科学G辑,2006,36(4):427～436.
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[5]傅华,刘仓理,王文强,李涛.冲击动力学中离散元与有限元相结合的计算方法研究[J].高压物理学报,2009,20(4):379～386.
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[9]Ted Belytschko,Wing Kam Liu,Brian Moran.Nonlinear FiniteElements for Continua and Structures[M]:John Wiley&SonLtd.,2000.
[10]Ted Belytschko,L.Schwer.Large displacement transient analysisof space frames[J].International Journal for Numerical Methodsin Engineering,1977(11):65～84.
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[14]Ted Belytschko,Neal M.O.Contact-impact by the pinballalgorithm with penalty and Lagrangian methods[J].InternationalJournal for Numerical Methods in Engineering,1991,131:547～572.
[2]黄庆华.地震作用下钢筋混凝土框架结构空间倒塌反应分析[D].同济大学,2006.
[3]宣纲,顾祥林,吕西林.强震作用下混凝土框架结构倒塌过程的数值分析[J].地震工程与工程振动,2003,23(6):24～30.
[4]胥建龙,唐志平.离散元与有限元结合的多尺度方法及其应用[J].计算物理,2003,第06期.
[5]傅华,刘仓理,王文强,李涛.冲击动力学中离散元与有限元相结合的计算方法研究[J].高压物理学报,2009,20(4):379～386.
[6]李世海,刘晓宇,张磊,等.基于连续介质力学模型离散元方法研究进展[C].中国力学学会学术大会(2005).
[7]ROBERT D Cook,DAVID S Malkus,MICHAEL E Plesha,etal.Concepts and applications of finite element analysis[M].NewYork:John Wiley&Sons,2001.
[8]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.
[9]Ted Belytschko,Wing Kam Liu,Brian Moran.Nonlinear FiniteElements for Continua and Structures[M]:John Wiley&SonLtd.,2000.
[10]Ted Belytschko,L.Schwer.Large displacement transient analysisof space frames[J].International Journal for Numerical Methodsin Engineering,1977(11):65～84.
[11]Ted Belytschko,Lin J.and Tsay C.S.Explicit algorithms for thenonlinear dynamics of shells[J].Computer Methods in AppliedMechanics and Engineering,1984,42:225～251.
[12]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.
[13]王福军.冲击接触问题有限元法并行计算及其工程应用[D].清华大学,2000.
[14]Ted Belytschko,Neal M.O.Contact-impact by the pinballalgorithm with penalty and Lagrangian methods[J].InternationalJournal for Numerical Methods in Engineering,1991,131:547～572.
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