一维问题的等效远置动力人工边界条件
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摘要
在土-结构动力相互作用分析中,黏性人工边界条件和黏弹性人工边界条件虽具有计算效率和精度较高的优点,但施加边界单元的工作量较大;远置边界虽然具有处理技术简单、精度高等优点,但又存在计算成本高的问题。为克服黏性人工边界和黏弹性人工边界施加边界黏弹性单元工作量大、远置边界计算成本高的缺点,基于波的传播理论和波在介质交界面上的反射、透射原理,通过设置完全透射层并大大降低波在透射层的传播速度的方法,提出了一种等效远置动力人工边界条件并对其进行数值验证分析。研究结果表明,所提出的等效远置动力人工边界条件仅需通过合理选取透射层的参数,即可实现反射波向无限地基传播的模拟,具有精度和效率较好、不需施加边界单元工作量等优点,可应用到土-结构动力相互作用分析当中。
In the analysis of dynamic soil-structure interaction,viscous artificial boundary condition,viscoelastic artificial boundary condition and far-field artificial boundary are often used to simulate the scattered wave propagating in infinite base.Viscous artificial boundary condition and viscoelastic artificial boundary condition have many advantages such as low computing cost and good accuracy;but amount of labor work of applying boundary elements is heavy;although far-field boundary saves the work of applying boundary elements and can provide highly accurate results;it requires expensive computing cost.In order to address the problem of high labor cost in viscous artificial boundary condition and viscoelastic artificial boundary condition and high computing cost in far-field boundary,an equivalent far-field artificial boundary condition is proposed based on the wave propagating theory and the reflection and transmission principle of wave on the interface of medium by setting a fully-transmitting layer and lowering the speed of wave considerably propagating within it.Then numerical simulations and studies of factors affecting accuracy for equivalent far-field artificial boundary condition are conducted with FEM.Researches show that equivalent far-field artificial boundary can be set up only by setting rational mass and Young’s modulus parameters in transmitting boundary layer to simulate reflected wave propagating in infinite base.Equivalent far-field artificial boundary has many advantages such as good accuracy and efficiency and saving the labor work of applying boundary elements;so it can be applied to the analysis of dynamic soil-structure interaction.
In the analysis of dynamic soil-structure interaction,viscous artificial boundary condition,viscoelastic artificial boundary condition and far-field artificial boundary are often used to simulate the scattered wave propagating in infinite base.Viscous artificial boundary condition and viscoelastic artificial boundary condition have many advantages such as low computing cost and good accuracy;but amount of labor work of applying boundary elements is heavy;although far-field boundary saves the work of applying boundary elements and can provide highly accurate results;it requires expensive computing cost.In order to address the problem of high labor cost in viscous artificial boundary condition and viscoelastic artificial boundary condition and high computing cost in far-field boundary,an equivalent far-field artificial boundary condition is proposed based on the wave propagating theory and the reflection and transmission principle of wave on the interface of medium by setting a fully-transmitting layer and lowering the speed of wave considerably propagating within it.Then numerical simulations and studies of factors affecting accuracy for equivalent far-field artificial boundary condition are conducted with FEM.Researches show that equivalent far-field artificial boundary can be set up only by setting rational mass and Young’s modulus parameters in transmitting boundary layer to simulate reflected wave propagating in infinite base.Equivalent far-field artificial boundary has many advantages such as good accuracy and efficiency and saving the labor work of applying boundary elements;so it can be applied to the analysis of dynamic soil-structure interaction.
引文
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[9]张波,李术才,杨学英,等.三维黏弹性人工边界地震波动输入方法研究[J].岩土力学,2009,30(3):774-778.ZHANG Bo,LI Shu-cai,YANG Xue-ying,et al.Research on seismic wave input with three-dimensional viscoelastic artificial boundary[J].Rock and Soil Mechanics,2009,30(3):774-778.
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[11]LIU J B,LU Y D.A direct method for analysis of dynamic soil-structure interaction based on interface idea[C]//Proceedings of the Chinese-Swiss Workshop on Soil-Structure Interaction.Amsterdam:Elsevier Science B V,1997.
[12]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,ASCE,1994,120(1):25-42.
[13]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.
[2]KOYAMA D.An artificial boundary condition for the numerical computation of scattering waves[C]//12th International Conference on Domain Decomposition Methods.Chiba:DDM.org,2001.
[3]LYSMER J,KULEMEYER R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mechanics Division,ASCE,1969,95(4):859-878.
[4]LYSMER J,KUHLEMEYER R L.Finite element method accuracy for wave propagation problems[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1973,99(5):421-427.
[5]JIAO Y Y,ZHANG X L,ZHAO J,et al.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].Rock Mechanics and Mining Sciences,2007,44:1070-1076.
[6]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,1994,120(1):25-42.
[7]ZHANG Q,GUO B Z.Stabilization of an elastic plate with viscoelastic boundary conditions[J].Journal of Optimization Theory and Applications,2004,122(3):669-690.
[8]OLIVIER CHIELLO,FRANCK C SGARD,NOUREDDINE ATALLA.A modal synthesis approach to investigate the influence of viscoelastic boundary conditions on the sound radiated from a plate backed cavity[J].The Journal of the Acoustical Society of America,1999,105(2):1087-1087.
[9]张波,李术才,杨学英,等.三维黏弹性人工边界地震波动输入方法研究[J].岩土力学,2009,30(3):774-778.ZHANG Bo,LI Shu-cai,YANG Xue-ying,et al.Research on seismic wave input with three-dimensional viscoelastic artificial boundary[J].Rock and Soil Mechanics,2009,30(3):774-778.
[10]ALTEMAN Z S,JR KARAL F C.Propagation of elastic waves in layered media by finite-difference methods[J].Bulletin of the Seismological Society of America,1968,58(1):367-398.
[11]LIU J B,LU Y D.A direct method for analysis of dynamic soil-structure interaction based on interface idea[C]//Proceedings of the Chinese-Swiss Workshop on Soil-Structure Interaction.Amsterdam:Elsevier Science B V,1997.
[12]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,ASCE,1994,120(1):25-42.
[13]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.
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