时间卷积的局部高阶弹簧-阻尼-质量模型
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摘要
土-结相互作用的时域有限元分析中,力和位移时间卷积关系的局部化处理是建立精确无限域模拟方法的关键。应用物理模型化方法局部化时间卷积,提出一种新的高阶弹簧-阻尼-质量模型,推导了模型的时域、频域方程和相应的标准方程,建立了两类方程参数的转换关系。基于线性系统稳定性理论提出模型系统运动稳定的充分必要条件,并基于罚函数法和遗传-单纯形法建立了考虑模型稳定性的参数识别方法。基于该文参数识别方法的高阶弹簧-阻尼-质量模型系统、简洁,能够在动力有限元程序或商用软件中简单、容易的实现,形成动力稳定的土-结相互作用系统,可以采用显式时间积分求解。弹性地基表面半无限杆问题的分析以及与几种现有方法的比较研究表明该文模型及参数识别方法的有效性。
The localization of time convolution relation of generalized force and displacement has been the key to the construction of an pricise and infinite-domain FEM model used for the time-domain soil-structure-interaction analysis.The physical model method is used in this paper to localize time convolution as it is compatible to FEM.A novel model of high-order spring-dashpot-mass(HSDMM) is constructed using the time-and frequency-domain equations as well as the corresponding normal equations.The transformation relation for the parameters used in these two types of equations is also otained.The sufficient and necessary dynamic stability conditions for the proposed model are proposed,and a parameter identification method(PIM) considering stability condition is developed based on the penalty function and the genetic-simplex algorithm.The systemic and concise HSDMM with the proposed PIM can be readily incorporated into a dynamic commercial software and the established dynamically stable soil-structure interaction problem can be solved even using an explicit time stepping integration.Finally,the performance of HSDMM with the proposed PIM is evaluated by analyzing a semi-infinite rod on elastic foundation with it and comparing the results to the results obtained with several existing models.
The localization of time convolution relation of generalized force and displacement has been the key to the construction of an pricise and infinite-domain FEM model used for the time-domain soil-structure-interaction analysis.The physical model method is used in this paper to localize time convolution as it is compatible to FEM.A novel model of high-order spring-dashpot-mass(HSDMM) is constructed using the time-and frequency-domain equations as well as the corresponding normal equations.The transformation relation for the parameters used in these two types of equations is also otained.The sufficient and necessary dynamic stability conditions for the proposed model are proposed,and a parameter identification method(PIM) considering stability condition is developed based on the penalty function and the genetic-simplex algorithm.The systemic and concise HSDMM with the proposed PIM can be readily incorporated into a dynamic commercial software and the established dynamically stable soil-structure interaction problem can be solved even using an explicit time stepping integration.Finally,the performance of HSDMM with the proposed PIM is evaluated by analyzing a semi-infinite rod on elastic foundation with it and comparing the results to the results obtained with several existing models.
引文
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[22]Lathi B T.Linear systems and signals[M].2nd ed.New York:Oxford University Press,2004.
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[25]Hughes T J R.The finite element method:linear static and dynamic finite element analysis[M].Englewood Cliffs,NJ:Prentice-Hall,1987.
[26]杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37―43.Du Xiuli,Wang Jinting.An explicit difference formulation of dynamic response calculation of elastic structure with damping[J].Engineering Mechanics,2000,17(5):37―43.(in Chinese)
[2]Wolf J P.Foundation vibration analysis using simple physical models[M].Englewood Cliffs:Prentice-Hall,1994.
[3]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002.Liao Zhenpeng.Introduction to wave motion theories for engineering[M].2nd ed.Beijing:Science Press,2002.(in Chinese)
[4]Lysmer J,Kuhlemeyer R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mechanics Division ASCE,1969,95(EM4):869―877.
[5]Hagstrom T.Radiation boundary conditions for the numerical simulation of waves[J].Acta Numerica,1999,8:47―106.
[6]Hagstrom T.New results on absorbing layers and radiation boundary conditions[R]//Ainsworth M,Davies P,Duncan D,Martin P,Rynne B.Topics in Computational Wave Propagation.New York:Spring-Verlag,2003:1―42.
[7]Wolf J P.Consistent lumped-parameter models for unbounded soil:physical representation[J].Earthquake Engineering and Structural Dynamics,1991,20:11―32.
[8]Wolf J P.Consistent lumped-parameter models for unbounded soil:frequency-independent stiffness,damping and mass matrices[J].Earthquake Engineering and Structural Dynamics,1991,20:33―41.
[9]Wu W-H,Lee W-H.Systematic lumped-parameter models for foundations based on polynomial-fraction approximation[J].Earthquake Engineering and Structural Dynamics,2002,31:1383―1412.
[10]Wu W-H,Lee W-H.Nested lumped-parameter models for foundation vibrations[J].Earthquake Engineering and Structural Dynamics,2004,33:1051―1058.
[11]景立平,廖振鹏,邹经相.多次透射公式的一种高频失稳机制[J].地震工程与工程振动,2002,22(1):7―13.Jing Liping,Liao Zhenpeng,Zou Jingxiang.A high-frequency instability mechanism in numerical realization of multi-transmitting formula[J].Earthquake Engineering and Engineering Vibration,2002,22(1):7―13.(in Chinese)
[12]景立平,吴兆营,邹经相.近场波动数值模拟稳定性问题分析[J].地震工程与工程振动,2002,22(2):17―21.Jing Liping,Wu Zhaoying,Zou Jingxiang.Stability analysis for numerical simulation of near-field wave motion[J].Earthquake Engineering and Engineering Vibration,2002,22(2):17―21.(in Chinese)
[13]Liu J,Lu Y.A direct method for analysis of dynamic soil-structure interaction based on interface idea[C]//Zhang Chuhan,Wolf J P.Proceedings of the Chinese-Swiss Workshop on Dynamic Soil-Structure Interaction.Beijing:International Academic Publishers,1997.
[14]刘晶波,王振宇,杜修力,杜义欣.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46―51.Liu Jingbo,Wang Zhenyu,Du Xiuli,Du Yixin.Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46―51.(in Chinese)
[15]Liu Jingbo,Li Bin.A unified viscous-spring artificial boundary for3-D static and dynamic applications[J].Science in China Ser.E,2005,48(5):570―584.
[16]Liu J,Du Y,Du X,Wang Z,Wu J.3D viscous-spring artificial boundary in time domain[J].Earthquake Engineering and Engineering Vibration,2006,5(1):93―102.
[17]Kellezi L.Local transmitting boundaries for transient elastic analysis[J].Soil Dynamics and Earthquake Engineering,2000,19:533―547.
[18]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49―56.Du Xiuli,Zhao Mi,Wang Jinting.A stress artificial boundary in FEA for near-field wave problem[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):49―56.(in Chinese)
[19]Deeks A J,Randolph M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics ASCE,1994,120(1):25―42.
[20]Alpert B,Greengard L,Hagstrom L.Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation[J].SIAM Journal on Numerical Analysis,2000,37(4):1138―1164.
[21]Alpert B,Greengard L,Hagstrom L.Nonreflecting boundary conditions for the time-dependent wave equation[J].Journal of Computational Physics,2002,180:270―296.
[22]Lathi B T.Linear systems and signals[M].2nd ed.New York:Oxford University Press,2004.
[23]Goldberg D E.Genetic algorithms in search,optimization and machine learning[M].Reading,MA:AddisonWesley,1989.
[24]Lagarias J C,Reeds J A,Wright M H,Wright P E.Convergence properties of the Nelder-Mead simplex method in low dimensions[J].SIAM Journal on Optimization,1998,9(1):112―147.
[25]Hughes T J R.The finite element method:linear static and dynamic finite element analysis[M].Englewood Cliffs,NJ:Prentice-Hall,1987.
[26]杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37―43.Du Xiuli,Wang Jinting.An explicit difference formulation of dynamic response calculation of elastic structure with damping[J].Engineering Mechanics,2000,17(5):37―43.(in Chinese)
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