摘要
近些年粘弹性人工边界被提出,利用有限元通用软件ANSYS中提供的弹簧-阻尼单元(Spring-damper),可以较容易的模拟粘弹性人工边界条件。由于该方法简单,又具有较好的精度;更重要的是它可以方便地在通用的商业软件中实现,近些年它在结构-地基动力相互作用分析问题中得到了有效的应用。通常这些应用是针对一个结构物的情况,即所谓单源散射。
但有些情况下,例如在多跨桥梁、铁路路基等延伸较长的结构中,桥梁基础或轨枕有多个并且相距可能很远;这种情况是多源散射问题。如果在这种情况下仍然采用单源散射问题的粘弹性人工边界,会产生误差。而粘弹性人工边界的精度是评价其工程应用价值的一个重要指标。
针对这种情况,本文在原有粘弹性人工边界的基础上,提出了多源散射粘弹性人工边界,该方法适用于具有多点内源输入荷载和多点地震动输入的情况。本文用有限元软件ANSYS中提供的弹簧-阻尼单元(Spring-damper)模拟粘弹性人工边界条件,并进行了数值计算。算例表明,与单源散射粘弹性人工边界相比本文方法能够有效地提高粘弹性人工边界的计算精度。
The viscous-spring artificial boundary is proposed in recent years, which is realized easily by utilizing the Spring-damper cell in finite element software of ANSYS. The combination method of the finite element method and the viscous-spring boundary is used effectively in dynamic soil-structure interaction because it's simply ,high accuracy and convenient actualization in current commercial software in recent years. The method is applied in the situation of single scattering source.
But in the long-outspread structure of multiple-span bridge and railway roadbed, the distance between of bridge foundations and sleepers may be far ,which are called multi-points scattering problem. The error would be caused if the viscous-spring artificial boundary of single scattering source is used in above situations. Meanwhile, the artificial accuracy is an important criterion which evaluate its application in engineering.
On the basis of prevenient viscous-spring artificial boundary, the viscous-spring artificial boundary of multi-points scattering source is proposed, which is suitable for the input of multi-points scattering and seismic wave. The numerical calculate is carried by simulating the viscous-spring artificial boundary with the Spring-damper cell in ANSYS. The results indicate the proposed method in the paper can improve the accuracy of viscous-spring artificial boundary compared with the situation of single scattering source.
引文
[1]廖振鹏.工程波动理论导论(2002).科学出版社,2002
[2]Z.S.Alterman and F.C.J.Karal.Propagation of Elastic Waves in Layered Media by Finite-Difference Methods.Bulletin of the Seismological Society of America.1968,58:367-398
[3]Lysmer J,Kulemeyer RL.Finite dynamic model for infinite media.Journal of Engineering Mechanics,ASCE,1969,95:759-877
[4]Deeks A J,Randolph MF.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,ASCE,1994,120(1):25-42
[5]Lin Jingbo,Lu Yandong.A direct method for analysis of dynamic soil-structure interaction based on interface idea[J]..In:Zhang Chuhan,Wolf JP edit.Dynamic Soil-structure Interaction.International Academia Publishers,1997:258-273
[6]刘品波,吕彦尔.结构-地基动力相互作用问题分析的一种直接方法.土木工程学报,1998,31(3):55-64.
[7]王振宁,刘品波.成层地基非线性波动问题人工边界与波动输入研究.岩土力学与工程学报.2004,23(7):1169-1173
[8]刘品波,王振宁,杜修力.波动问题中的三维时域粘弹性人工边界.工程力学
[9]中华人民共和国国家标准.核电厂抗震设计规范(GB50267-97).中国计划出版社,1998.
[10]Zienkiewicz OC.Computational Geomechanics with Special Reference to Earthquake Engineering.John Wiley & Sons,1998
[11]Modaressi H,Benzenati I.Absorbing boundary element for dynamic analysis of two-phase media[C].Proceedings of the World Conference on Earthquake Engineering,1992.1157
[12]Degrande G,De Roeck G.An absorbing boundary condition for wave propagation in saturated poroelastic media[M].Part Ⅰ:Formulation and efficiency evaluation.Soil Dynamics and Earthquake Engineering,1993,12:411-42 l
[13]Akiyoshi T,Fuchida K,Fang HL.Absorbing boundary conditions for dynamic analysis of fliud-saturated porous media[J]..Soil Dynamics and Earthquake Engineering,1994,13:387-397
[14]Gajo A,Saetta A,Vitaliani R.Silent boundary conditions for wave propagation in saturated porous media[J]..International Journal for Numerical and Analytical Methods in Geomechanics,1996,13:253-273
[15]Akiyoshi T,Sun X,Fuchida K.General absorbing conditions for dynamic analysis of fluid-saturated porous media.Soil Dynamics and Earthquake Engineering,1998,17:397-406
[16]邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法[J].地球物理学报,2000,43(2):267-275
[17]Zohra Zerfa,Benjamin Loret.A viscous boundary for transient analyses of saturated porous media[J].Earthquake Engineering and Structural Dynamics,2004,33:89-110
[18]王子辉,赵成刚,董亮.流体饱和多孔介质粘弹性动力人工边界[J].力学学报,2006,38(5):607-611
[19]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.The Journal of the Acoustical Society of America,1956,28(2):168-191
[20]Biot M A.Generalized theory of acoustic propagation in porous dissipative media.The Journal of the Acoustical Society of America,1962,34(9):1254-1264
[21]Biot M A,Willis D G.The elastic coefficients of the theory of consolidation.Journal of Applied Mechanics,1957,24(4):594-601.
[22]门福录.波在饱水孔隙弹性介质中的传播.地球物理学报,1965,14(2):107-114
[23]门福录.波在饱含流体的孔隙介质中的传播问题.地球物理学报,1981,24(1):65-75
[24]Levy T.Propagation of waves in a fluid-saturated porous elastic solid.International Journal of Engineering Science,1979,17(9):1005-1014
[25]Auriault J L.Dynamic behaviour of a porous medium saturated by a Newtonian fluid.International Journal of Engineering Science,1980,18(6):775-785
[26]Zienkiewicz O C.Basic formulation of static and dynamic behaviour of soil and other porous media.Numerical Methods in Geomechanics,edited by J.B.Martins,D.Reidl,1982:39-55
[27]Zienkiewicz O C,Shiomi T.Dynamic behaviour of saturated porous media;the generalized Biot formulation and its numerical solution.International Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1):71-96
[28]imon B R,Zienkiewicz O C,Paul D K.An analytical solution for the transient response of saturated porous elastic solids.International Journal for Numerical and Analytical Methods in Geomechanics,1984,8(4):381-398
[29]陈龙珠,吴世明,曾国熙.弹性波在饱和土层中的传播.力学学报,1987,19(3):276-283
[30]V.N.尼古拉也夫斯基.流体饱和的岩士力学.Z.P.巴赞特编著,岩土和混凝土力学.重庆:重庆大学出版社,1991:211-225
[31]Bowen R M.混合物理论.南京:江苏科技出版社,1983
[32]Bowen R M,Reinicke K M.Plane progressive waves in a binary mixture of linear elastic materials.Journal ofAppliedMechanics,1978,45(3):493-499
[33]Atkin R J,Craine R E.Continuum theories of mixtures:basic theory and historical development.Quarterly Journal of Mechanics and Applied Mathematics,1976,29(2):209-244
[34]Bowen R M Compressible porous media models by use of the theory of mixtures.International Journal of Engineering Science,1982,20(6):697-735
[35]Bowen R M.Plane progressive waves in a heat conducting fluid saturated porous material with relaxing porosity.Acta Mechanica,1983,46(1-4):189-206
[36]Prevost J H.Mechanics of continuous porous media.International Journal of Engineering Science,1980,18(6):787-800
[37]Prevost J H.Nonlinear transient phenomena in saturated porous media.Computer Methods in Applied Mechanics and Engineering,1982,30(1):3-18
[38]苗天德,朱久江,丁伯阳.对饱和多孔介质波动问题中本构关系的探讨.力学学报,1995,27(5)536-543
[39]Mei C C,Foda M A.Wave-induced responses in a fluid-filled poro-elastic solid with a free surface — a boundary layer theory.Geophysical Journal of the Royal Astronomical Society,1981,66(3):597-631
[40]李向维,李向约.饱水孔隙介质的质量耦合波动问题.应用数学和力学,1989,10(4):309-314
[41]Garg S K,Nayfeh A H,Good A J.Compressional waves in fluid-saturated elastic porous media.Journal of Applied Physics,1974,45(5):1968-1974
[42]Garg S K,Brownell D H,Pritchett J W,Herrmann R G.Shock-wave propagation in fluid-saturated porous media.Journal of Applied Physics,1975,46(2):702-713
[43]Ghaboussi J,Wilson E L.Variational formulation of dynamics of fluid-saturated porous elastic solids.Journal of the Engineering Mechanics Division,ASCE,1972,98(EM4):947-963
[44]Ghaboussi J,Wilson E L.Seismic analysis of earth dam-reservoir systems.Journal of the Soil Mechanics and Foundations Division,ASCE,1973,99(SM10):849-886
[45]Ghaboussi J,Dikmen S U.Liquefaction analysis of horizontally layered sands.Journal of the Geotechnical Engineering Division,ASCE,1978,104(3):341-356
[46]Simon B R,Wu J S S,Zienkiewicz O C,Paul D K.Evaluation ofu-w and u-n finite element methods for the dynamic response of saturated porous media using one-dimensional models.International Journal for Numerical and Analytical Methods in Geomechanics,1986,10(5):461-482
[47]Simon B R,Wu J S S,Zienkiewicz O C.Evaluation of higher order,mixed and Hermitean finite element procedures for dynamic analysis of saturated porous media using one-dimensional models.International Journal for Numerical and Analytical Methods in Geomechanics,1986,10(5):483-499
[48]Prevost J H.Wave propagation in fluid-saturated porous media:an efficient finite element procedure.Soil Dynamics and Earthquake Engineering,1985,4(4):183-202
[49]Yiagos A N,Prevost J H.Two-phase elasto-plastic seismic response of earth dam:theory.Soil Dynamics and Earthquake Engineering,1991,10(7):357-370
[50]Sandhu R S,Hong S J.Dynamics of fluid-saturated soil variational formulation.International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(3):241-255
[51]Sandhu R S,Shaw H L,Hong S J.Three-field finite element procedure for analysis of elastic wave propagation through fluid-saturated soils.Soil Dynamics and Earthquake Engineering,1990,9(2):58-65
[52]Hirai H.Analysis of Rayleigh waves in saturated porous elastic media by finite element method.Soil Dynamics and Earthquake Engineering,1992,11(6):311-326
[53]Bougacha S,Tassoulas J L,Roesset J M.Analysis of foundations on fluid-filled poroelastic stratum.Journal ofEngineeringMechanics,ASCE,1993,119(8):1632-1648
[54]Bougacha S,Tassoulas J L.Seismic analysis of gravity dams.Journal of Engineering Mechanics,ASCE,1991,117(8):1826-1850
[55]Bougacha S,Roesset J M,Tassoulas J L.Dynamic stiffness of foundations on fluid-filled poroelastic stratum.Journal of Engineering Mechanics,ASCE,1993,119(8):1649-1662
[56]Aubry D,Modaressi H.A model for the non linear dynamic analysis of saturated soils.Rev.Franc.Geotech.,1989,46:43-75
[57]Yazdi J T,Valliappan S,Zhao Chongbin.Analytical and numerical solutions for wave propagation in water-saturated porous layered half-space.Soil Dynamics and Earthquake Engineering,1994,13(4):249-257
[58]Khalili N,Valliappan S,Yazdi J T,Yazdchi M.1D infinite element for dynamic problems in saturated porous media.Communications in Numerical Methods in Engineering,1997,13(9):727-738
[59]Khalili N,Yazdchi M,Valliappan S.Wave propagation analysis of two-phase saturated porous media using coupled finite-infinite element method.Soil Dynamics and Earthquake Engineering,1999,18(8):533-553
[60]崔杰.砂土液化过程的动力分析.硕士学位论文.国家地震局工程力学研究所,1987
[61]崔杰等.砂土液化的计算机仿真.地震科学联合基金成果报告.国家地震局工程力学研究所,1995
[62]张洪武,何扬,李锡夔.饱和多孔介质半无限域动力一渗流分析中的非反射边界法.岩土工程学报,1990,12(4):49-56
[63]钱令希,钟万勰,张洪武.二相饱和海洋土壤地基与平台结构相互作用的动力有限元分析.(国家自然科学基金会)海洋工程中的力学问题汇报研讨会,上海,1990,12
[64]张洪武,钟万勰,钱令希.饱和土动力固结分析中的变分原理.岩士土程学报,1992,14(3):20-29
[65]徐文骏,郭建.流体饱和多孔介质中弹性波的数值模拟.地球物理学报,1994,37(Supp.Ⅱ):424-433
[66]秦小军,陈少林,曾心传.二维饱和孔隙介质的二场有限元方法.地壳形变与地震,1999,19(2)60-69
[67]邵秀民,蓝忠凌.流体饱和多孔介质波动方程的有限元解法.地球物理学报,2000,43(2):264-278
[68]赵成刚,王进廷,史培新,李伟华.流体饱和两相多孔介质动力反应分析的显式有限元法.岩土工程学报,2001,23(2):178-182
[69]杨军,宋二祥,陈肇元.饱和土动力反应中两类压缩波的独立作用分析,岩土力学,2001.2(2)
[70]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
[71]杜修力.局部解耦的时域波分析方法[J].世界地震工程,2000,16(3):22-26
[72]李小军.非线性场地地震反应分析方法的研究.博士研究生学位论文.国家地震局工程力学研究所,1993年3月