地震中结构碰撞的接触单元模型的改进算法
|
摘要
针对用于地震碰撞分析的接触单元模型提出了一种改进求解方法。该方法把碰撞问题等效为一个弹簧—振子模型,由振子、弹簧和阻尼器构成。振子的运动过程代表碰撞的压缩和恢复过程。可以通过对运动方程的求解,得到相对压入量、相对压入速度、碰撞力、碰撞持续时间及其相互关系。该求解方法没有像常用求解方法假设压缩过程和恢复过程中耗散能量相等或者相对压入速度绝对值相等,所以可以得到精确解或者无限接近精确解的近似解。在碰撞中能量耗散较小的情况下,Hertzdamp模型常用求解方法得到的结果接近精确解;而当能量耗散较大时,与精确解的差别就比较大。改进算法不论碰撞中能量耗散大或者小,都可以得到无限接近精确解的结果。因此,改进算法比常用算法更具优越性,尤其是对于存在大量能量耗散的地震碰撞问题。
To better study the issue,we presented an improved algorithm.In this algorithm,the impact issue is equivalent to a spring-oscillator model which contains an oscillator,a spring and a damper.The oscillator movement represents the compression phase and restitution phase of impact.By solving the motion equation,we got the penetration displacement,penetration velocity,impact force,impact time and their mutual relationship.The solution process did not carriy out the hypothesis that the energy dissipation or absolute speed during the restitution phase is the same as that during the compression phase,which was adopted by common solution methods.Therefore we can get the exact results or approximate results that are infinitely close to the exact results.In the case of small energy dissipation during the collision,Hertzdamp model results obtaind by common solution methods are close to the exact results.When the energy dissipation during the collision is large,the difference between them becomes obvious.Regardless of small or large energy dissipation during the collision,the improved algorithm can obtain the results which are infinitely close to the exact results.
To better study the issue,we presented an improved algorithm.In this algorithm,the impact issue is equivalent to a spring-oscillator model which contains an oscillator,a spring and a damper.The oscillator movement represents the compression phase and restitution phase of impact.By solving the motion equation,we got the penetration displacement,penetration velocity,impact force,impact time and their mutual relationship.The solution process did not carriy out the hypothesis that the energy dissipation or absolute speed during the restitution phase is the same as that during the compression phase,which was adopted by common solution methods.Therefore we can get the exact results or approximate results that are infinitely close to the exact results.In the case of small energy dissipation during the collision,Hertzdamp model results obtaind by common solution methods are close to the exact results.When the energy dissipation during the collision is large,the difference between them becomes obvious.Regardless of small or large energy dissipation during the collision,the improved algorithm can obtain the results which are infinitely close to the exact results.
引文
[1]GILARDI G,SHARF I.Literature survey of contactdynamics modeling[J].Mechanism and MachineTheory,2002,37(10):1213-1239.
[2]COURANT R,FRIEDRICHS K,LEVY J.Uber diepertieller differentzengleichuangen der mathmatischenphysic[J].Mathmatische Annalen,1928,100(1):32-74.
[3]BATHE K J,CHAUDHARY A.A solution methodfor planar and axisymmetric contact problems[J].International Journal for Numerical Methods inEngineering,1985,21(1):65-88.
[4]SIMO J C,WRIGGERS P.A perturbed lagrangianformulation for the finite element solutions of contactproblems[J].Comput Meth Appl Mech Engng,1985,50:163-180.
[5]PIETRZAK G,CURNIER A.Large deformationfrictional contact mechanics:continuum formulationand augmented Lagrangian treatment[J].ComputMeth Appl Mech Engng,1999,177(3-4):351-381.
[6]MUTHUKUMAR S,DESROCHES R.Evaluation ofimpact models for seismic pounding[C]//Proc of 13thWorld Conference on Earthquake Engineering.B.C.Canada:Vancouver,2004.
[7]HUNT K H,CROSSLEY F R E.Coefficient ofrestitution interpreted as damping in vibroimpact[J].Journal of Applied Mechanics(ASME),1975,42(2):440-445.
[8]MAHMOUD S,CHEN X J,JANKOWSKI R.Structural pounding models with hertz spring andnonlinear damper[J].Journal of Applied Science.2008,8(10):1850-1858.
[9]MUTHUKUMAR S,DESROCHES R.A Hertzcontact model with non-linear damping for poundingsimulation[J].Earthquake Engineering and StructuralDynamics,2006,35(8):811-828.
[10]MUTHUKUMAR S.A contact element approach withhysteresis damping for the analysis and design ofpounding in bridges[D].Dissertation:GeorgiaInstitute of Technology,2003.
[11]LANKARANI H M,NIKRAVESH P E.A contactforce model with hysteresis damping for impact analysisof multibody systems[J].Journal of MechanicalDesign(AMSE),1990,112(3):369-376.
[12]KOMODROMOS P.Simulation of the earthquake-induced pounding of seismically isolated buildings[J].Computers and Structures,2008,86(7-8):618-626.
[13]SHAKYA K,WIJEYEWICKREMA A C,OHMACHIT.Performance of reinforced concrete buildings duringseismic pounding considering soil-foundation interaction[C]//Proceedings of the Symposium on Development ofPractical Urban Earthquake Engineering Research forMitigation of Mega Earthquakes in the MetropolitanArea,Suzukakedai,Yokohama,Japan,March 25,2009:39-42.
[14]JANKOWSKI R.Earthquake-induced poundingbetween equal height buildings with substantiallydifferent dynamic properties[J].EngineeringStructures,2008,30(10):2818-2829.
[15]POLYCARPOU C P,KOMODROMOS P.Earthquake-induced poundings of a seismically isolatedbuilding with adjacent structures[J].EngineeringStructures,2010,32(7):1937-1951.
[16]金栋平,胡海岩.碰撞振动与控制[M].北京:科学出版社,2005.
[17]MAHMOUD S,CHEN X J,JANKOWSKI R.Structural pounding models with Hertz spring andnonlinear damper[J].Journal of Applied Sciences,2008,8(10):1850-1858.
[18]YE K,LI L,ZHU P H.A note on the Hertz contactmodel with nonlinear damping for pounding simulation[J].Earthquake Engng Struct Dyn,2009,38(9):1135-1142.
[19]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133.LI ZHONG-XIAN,YUE FU-QING,ZHOU LI.Equivalent kelvin impact model for pounding analysis ofbridges during earthquake[J].Engineering Mechanics,2008,25(4):128-132.
[20]岳福青.地震作用下隔震高架桥梁的碰撞反应及控制[D].天津大学,2007.
[2]COURANT R,FRIEDRICHS K,LEVY J.Uber diepertieller differentzengleichuangen der mathmatischenphysic[J].Mathmatische Annalen,1928,100(1):32-74.
[3]BATHE K J,CHAUDHARY A.A solution methodfor planar and axisymmetric contact problems[J].International Journal for Numerical Methods inEngineering,1985,21(1):65-88.
[4]SIMO J C,WRIGGERS P.A perturbed lagrangianformulation for the finite element solutions of contactproblems[J].Comput Meth Appl Mech Engng,1985,50:163-180.
[5]PIETRZAK G,CURNIER A.Large deformationfrictional contact mechanics:continuum formulationand augmented Lagrangian treatment[J].ComputMeth Appl Mech Engng,1999,177(3-4):351-381.
[6]MUTHUKUMAR S,DESROCHES R.Evaluation ofimpact models for seismic pounding[C]//Proc of 13thWorld Conference on Earthquake Engineering.B.C.Canada:Vancouver,2004.
[7]HUNT K H,CROSSLEY F R E.Coefficient ofrestitution interpreted as damping in vibroimpact[J].Journal of Applied Mechanics(ASME),1975,42(2):440-445.
[8]MAHMOUD S,CHEN X J,JANKOWSKI R.Structural pounding models with hertz spring andnonlinear damper[J].Journal of Applied Science.2008,8(10):1850-1858.
[9]MUTHUKUMAR S,DESROCHES R.A Hertzcontact model with non-linear damping for poundingsimulation[J].Earthquake Engineering and StructuralDynamics,2006,35(8):811-828.
[10]MUTHUKUMAR S.A contact element approach withhysteresis damping for the analysis and design ofpounding in bridges[D].Dissertation:GeorgiaInstitute of Technology,2003.
[11]LANKARANI H M,NIKRAVESH P E.A contactforce model with hysteresis damping for impact analysisof multibody systems[J].Journal of MechanicalDesign(AMSE),1990,112(3):369-376.
[12]KOMODROMOS P.Simulation of the earthquake-induced pounding of seismically isolated buildings[J].Computers and Structures,2008,86(7-8):618-626.
[13]SHAKYA K,WIJEYEWICKREMA A C,OHMACHIT.Performance of reinforced concrete buildings duringseismic pounding considering soil-foundation interaction[C]//Proceedings of the Symposium on Development ofPractical Urban Earthquake Engineering Research forMitigation of Mega Earthquakes in the MetropolitanArea,Suzukakedai,Yokohama,Japan,March 25,2009:39-42.
[14]JANKOWSKI R.Earthquake-induced poundingbetween equal height buildings with substantiallydifferent dynamic properties[J].EngineeringStructures,2008,30(10):2818-2829.
[15]POLYCARPOU C P,KOMODROMOS P.Earthquake-induced poundings of a seismically isolatedbuilding with adjacent structures[J].EngineeringStructures,2010,32(7):1937-1951.
[16]金栋平,胡海岩.碰撞振动与控制[M].北京:科学出版社,2005.
[17]MAHMOUD S,CHEN X J,JANKOWSKI R.Structural pounding models with Hertz spring andnonlinear damper[J].Journal of Applied Sciences,2008,8(10):1850-1858.
[18]YE K,LI L,ZHU P H.A note on the Hertz contactmodel with nonlinear damping for pounding simulation[J].Earthquake Engng Struct Dyn,2009,38(9):1135-1142.
[19]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133.LI ZHONG-XIAN,YUE FU-QING,ZHOU LI.Equivalent kelvin impact model for pounding analysis ofbridges during earthquake[J].Engineering Mechanics,2008,25(4):128-132.
[20]岳福青.地震作用下隔震高架桥梁的碰撞反应及控制[D].天津大学,2007.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心