无限域中的动力人工边界
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摘要
以二维出平面弹性波动为例,总结了几种常用的局部人工边界,即黏性边界、旁轴近似边界、Higdon边界、叠加边界、透射边界和黏弹性边界.分析了各种局部人工边界的优缺点,讨论它们之间的相互联系,并对它们的精度和适用性进行了比较.最后介绍了局部边界尤其是高阶边界可能存在的稳定性问题的研究进展.
Some local artificial boundaries for 2-D anti-plane wave motion were summarized, including the viscous boundary,paraxial axial approximation boundary, Higdon boundary, superposition boundary, transmitting boundary, and viscous-spring boundary. The advantages and disadvantages of the above boundaries and their relationships were discussed, and the precision and applicability of the boundaries were compared. Finally, some advances in the research of the stability of local boundaries, especially high-order boundaries, were introduced.
Some local artificial boundaries for 2-D anti-plane wave motion were summarized, including the viscous boundary,paraxial axial approximation boundary, Higdon boundary, superposition boundary, transmitting boundary, and viscous-spring boundary. The advantages and disadvantages of the above boundaries and their relationships were discussed, and the precision and applicability of the boundaries were compared. Finally, some advances in the research of the stability of local boundaries, especially high-order boundaries, were introduced.
引文
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[13]廖振鹏.工程波动理论导引[M].北京:科学出版社,1996.266—268.
[14]关慧敏,廖振鹏.局部透射边界和叠加边界的精度分析与比较[J].力学学报,1994,26(3):303—311.
[15]DeeksAJ,RandolphMF.Axisymmetrictime domaintransmittingboundaries[J].JournalofEngineeringMechanics,1994,120(1):25—42.
[16]刘晶波,吕彦东.结构地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55—64.
[17]高峰,马泽宝.无限地基的数值模拟[J].兰州铁道学院学报(自然科学版),2002,21(3):9—13.
[18]GustafssonB,KreissHO,SundstromA.Stabilitytheoryofdifferenceapproximationsformixedinitialboundaryvalueproblems[J].Ⅱ.MathComp,1972,26.
[19]HigdonRL.Numericalabsorbingboundaryconditionsforthewaveequation[J].MathComp,1987,49:65—90.
[20]StaceyR.Anexplicitunstablemodeintheclaytonandengquisttransparentboundaryprescription[J].BSSA,1991,81:694—698.
[21]LiaoZP,LiuJB.Numericalinstabilitiesofalocaltransmittingboundary[J].EarthqEngStructDyn,1992,21:65—77.
[22]廖振鹏,刘晶波.波动有限元模拟的基本问题[J].中国科学(B辑),1992,8:874—882.
[23]关慧敏,廖振鹏.局部人工边界稳定性的一种分析方法[J].力学学报,1996,28(5):376—380.
[24]李小军,廖振鹏.时域局部透射边界的计算漂移失稳[J].力学学报,1996,28(5):627—632.
[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.
[2]廖振鹏.法向透射边界[J].中国科学(E辑),1996,26(2):185—192.
[3]DominguezJ.Boundaryelementsindynamics[M].Southampton:ComputationalMechanicsPublications,1993.
[4]MedinaF,TailaoR.Finiteelementtechnicalsforproblemsofunboundeddomains[J].IntJNumeMethodsinEngi,1983,19(4):1209—1226.
[5]LysmerJ,KulemeyerRL.Finitedynamicmodelforinfinitemedia[J].JEngngMechDiv,ASCE,1969,95:859—877.
[6]ClaytonR,EngquistB.Absorbingboundaryconditionsforacousticandelasticwaveequations[J].BullSeismSocAmer,1977,76:1529—1540.
[7]ClaytonR,EngquistB.Absorbingboundaryconditionsforwaveequationmigration[J].Geophysics,1980,45:895—904.
[8]廖振鹏,黄孔亮,杨柏坡,等.暂态波透射边界[J].中国科学(A辑),1984,26(6):50—56.
[9]KauselE.Localtransmittingboundaries[J].JEngngMech,1988,114(6):1011—1027.
[10]HigdonRL.Absorbingboundaryconditionsfordifferenceapproximationstothemulti dimensionalwaveequation[J].MathComp,1986,47:437—459.
[11]SmithW.Anon reflectingplaneboundaryforwavepropagationproblems[J].JCompPhys,1973,15:492—503.
[12]KunarRR,MartiJ.Anon reflectingboundaryforexplicitcalculations[J].ComputationalMethodsforInfiniteDomainMedia StructureInteractio,ASME,AMD46,1981:183—204.
[13]廖振鹏.工程波动理论导引[M].北京:科学出版社,1996.266—268.
[14]关慧敏,廖振鹏.局部透射边界和叠加边界的精度分析与比较[J].力学学报,1994,26(3):303—311.
[15]DeeksAJ,RandolphMF.Axisymmetrictime domaintransmittingboundaries[J].JournalofEngineeringMechanics,1994,120(1):25—42.
[16]刘晶波,吕彦东.结构地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55—64.
[17]高峰,马泽宝.无限地基的数值模拟[J].兰州铁道学院学报(自然科学版),2002,21(3):9—13.
[18]GustafssonB,KreissHO,SundstromA.Stabilitytheoryofdifferenceapproximationsformixedinitialboundaryvalueproblems[J].Ⅱ.MathComp,1972,26.
[19]HigdonRL.Numericalabsorbingboundaryconditionsforthewaveequation[J].MathComp,1987,49:65—90.
[20]StaceyR.Anexplicitunstablemodeintheclaytonandengquisttransparentboundaryprescription[J].BSSA,1991,81:694—698.
[21]LiaoZP,LiuJB.Numericalinstabilitiesofalocaltransmittingboundary[J].EarthqEngStructDyn,1992,21:65—77.
[22]廖振鹏,刘晶波.波动有限元模拟的基本问题[J].中国科学(B辑),1992,8:874—882.
[23]关慧敏,廖振鹏.局部人工边界稳定性的一种分析方法[J].力学学报,1996,28(5):376—380.
[24]李小军,廖振鹏.时域局部透射边界的计算漂移失稳[J].力学学报,1996,28(5):627—632.
[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.
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