考虑横缝影响的拱坝动力分析
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摘要
本文在求解三维弹性静力摩擦接触问题的有效方法-非光滑方程组方法的基础上,通过能够近似满足动量、动能守恒条件的速度、加速度的修正方法,将该方法推广到动力接触问题的求解中,以考虑地震时拱坝中横缝的开合、错动对坝体动力响应的影响。同时文中采用由多次透射公式表示的人工边界条件来考虑坝-基动力相互作用的影响。数值算例中分析了横缝的数目和布置位置对拱坝动力响应的影响。
In this paper, the dynamic contact problem resulted from sticking, separate and sliding occurred in the contraction joints is simulated by the non-smooth equation method combined with the consideration of the balance of momentum and kinetic energy at the current of impact. The artificial boundary condition expressed by multi-transmitting formula is adopted to simulate the propagation of the scatter wave to the infinite. Implicit-explicit integration scheme is used for the equilibrium equation of the arch dam-foundation system. The effects of the number and position of the contraction joints on the dynamic response of arch dam are studied.
In this paper, the dynamic contact problem resulted from sticking, separate and sliding occurred in the contraction joints is simulated by the non-smooth equation method combined with the consideration of the balance of momentum and kinetic energy at the current of impact. The artificial boundary condition expressed by multi-transmitting formula is adopted to simulate the propagation of the scatter wave to the infinite. Implicit-explicit integration scheme is used for the equilibrium equation of the arch dam-foundation system. The effects of the number and position of the contraction joints on the dynamic response of arch dam are studied.
引文
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[24] Wen HwaCHEN,Pwu.TSAI.Finiteelementanalysisofelastodynamicslidingcontactproblemswithfriction[J].CompStruc,1986,22(6):925～938.
[25] 周正华,廖振鹏.多次透射公式的一种稳定实现措施[J].地震工程与工程振动,2001,21(1):9～14.
[26] 李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):74～79.
[27] 杜修力,王进廷.阻尼弹性结构动力计算的一种显式差分法[J].工程力学,2000,17(5):37～43.
[28] BinZhang,ApostolosSPapageorgiou,JohnLTassoulas.Ahybridnumericaltechnique,combiningthefinite elementandboundary elementmethods,formodelingthe3Dresponse[J].Bull.Seis.Soci.Amer.,1998,88(4):1036～1050.
[29] 徐艳杰,张楚汉,王光纶,等.小湾拱坝模拟实际横缝间距的非线性地震反应分析[J].水利学报,2001,(4):68～74.
[30] LucoJE,WongHL,DeBarrosFCP.Three dimensionresponseofacylindricalcanyoninalayeredhalf space[J].Earth.Engng.Struc.Dyna.,1990,19:799～817.
[2] DavidTL,MoruzianB,RazaqpurAG.Modellingofcontractionjointandshearslidingeffectsonearthquakeresponseofarchdam[J].Earth.Engrg.Struc.Dyna,1998,27:1023～1029.
[3] FenvesGL,MojtahediS,ReimerRB.Nonlinearearthquakeanalysisofarchdam/reservoir[A].EarthquakeEngineeringTenthWorldConference[C].Rotterdam:Balkense,1992.
[4] 赵光恒,杜成斌.分缝拱坝的地震响应分析[J].河海大学学报,1994,22(5):1～8.
[5] 徐艳杰.横缝配筋的拱坝地震非线性模型与无限地基影响研究[D].北京:清华大学,1999.
[6] 徐艳杰,张楚汉,金锋.非线性拱坝 地基动力相互作用的FE BE IBE模型[J].清华大学学报(自然科学版),1998,38(11):99～103.
[7] 刘晶波,王铎.考虑界面摩擦影响的可接触型裂纹动态分析的动接触力模型[A].弹性动力学最新进展[C].北京:科学出版社,1995.
[8] 杜修力,涂劲,陈厚群.有缝拱坝 地基系统非线性地震波动反应分析方法[J].地震工程与工程振动,2000,20(1):11～20.
[9] 涂劲.有缝界面的混凝土高坝-地基系统非线性地震波动反应分析[D].北京:中国水利水电科学研究院,1999.
[10] 李学文,陈万吉.三维接触问题的非光滑算法[J].计算力学学报,2000,17(1):43～49.
[11] 李学文.三维摩擦接触问题的非光滑方程组方法研究[D].大连:大连理工大学,2000.
[12] 廖振鹏.工程波动理论导引[M].北京:科学出版社,1996.
[13] HughesTJR,LiuWK.Implicit explicitfiniteelementsintransientanalysis:StablityTheory[J].J.Appl.Mech.,1978,45(6):371～374.
[14] HughesTJR,LiuWK.Implicit ExplicitFiniteElementsinTransientAnalyis:ImplementationandNumericalExamples[J].J.Appl.Mech.,1978,45(6):375～378.
[15] 钟万勰,张洪武,吴承伟.参变量变分原理及其在工程中的应用[M].北京:科学出版社,1995.
[16] AndersKlarbring.Amathematicalprogrammingapproachtothree dimensionalcontactproblemswithfriction[J].Comp.MethodsAppl.Mech.Engrg.1986,58:175～200.
[17] BMKwak.Complementarityproblemformulationofthree dimensionalfrictionalcontact[J].Trans.ASME,1991,58:134～140.
[18] 陈国庆,陈万吉,冯恩民.三维接触问题的非线性互补原理及算法[J].中国科学(A),1995,11:1181～1190.
[19] 陈国庆.三维弹性接触问题极小化数值解法-非线性互补模型和算法[D].大连:大连理工大学,1994.
[20] ChristensenPW,KlarbringA,JSPang,etal.Formulationandcomparisonofalgorithmforfrictionalcontactproblems[J].Int.J.Num.MethEngrg.,1998,42:145～173.
[21] HughesTJR,TaylorRL,SackmanJL,etal.Afiniteelementmethodforaclassofcontact impactproblem[J].CompMethApplMechEngrg,1976,8:249～276.
[22] 陈兵奎,李润方.冲击 动力接触问题有限元方法的几点注记[J].计算结构力学及其应用,1995,13(2):248～251.
[23] WHChen,JTYeh.Three dimensionalfiniteelementanalysisofstaticanddynamiccontactproblemswithfriction[J].CompStruc,1990,35(5):541～552.
[24] Wen HwaCHEN,Pwu.TSAI.Finiteelementanalysisofelastodynamicslidingcontactproblemswithfriction[J].CompStruc,1986,22(6):925～938.
[25] 周正华,廖振鹏.多次透射公式的一种稳定实现措施[J].地震工程与工程振动,2001,21(1):9～14.
[26] 李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):74～79.
[27] 杜修力,王进廷.阻尼弹性结构动力计算的一种显式差分法[J].工程力学,2000,17(5):37～43.
[28] BinZhang,ApostolosSPapageorgiou,JohnLTassoulas.Ahybridnumericaltechnique,combiningthefinite elementandboundary elementmethods,formodelingthe3Dresponse[J].Bull.Seis.Soci.Amer.,1998,88(4):1036～1050.
[29] 徐艳杰,张楚汉,王光纶,等.小湾拱坝模拟实际横缝间距的非线性地震反应分析[J].水利学报,2001,(4):68～74.
[30] LucoJE,WongHL,DeBarrosFCP.Three dimensionresponseofacylindricalcanyoninalayeredhalf space[J].Earth.Engng.Struc.Dyna.,1990,19:799～817.
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