摘要
随着现代化大城市的迅速发展,用地紧张的问题日益凸显,高层建筑以其能够节约城市用地,有效利用建筑空间等优点而逐渐被人们所采纳。而我国地处地震多发区,由此,高层建筑的抗震问题也日益受到工程界的关注。建筑结构的震害与地基条件密切相关,因此,在高层建筑的抗震设计和分析过程中考虑土-结构相互作用的影响十分必要。但对于现有的分析手段而言,计算成本高、过程繁琐、难以在实际工程中操作应用等因素是影响土-结构相互作用分析的关键难题,寻求一种高效便捷的数值模拟方法具有重要的理论意义和工程价值。因此,课题针对上述关键问题做了一系列的工作,主要的创新工作与成果有:
(1)对动态子结构法的研究现状及其分类进行了探讨。重点针对动态子结构法中的约束模态综合法进行了细致的讨论,并将其应用到土-高层建筑相互作用体系的模态分析以及弹性时程分析过程中,同时对非比例阻尼体系中阻尼矩阵的处理以及对接界面自由度的缩减方法进行了一些探讨,由算例的分析过程可知,约束模态综合法对于土-高层建筑相互作用体系的模态分析以及弹性时程分析是完全适用的;
(2)在深入分析约束模态综合法原理的基础上,定义了由不同主模态截断阶数产生的位移向量组成的线性空间,建立该空间上的一个函数,通过数学定理详细证明了该函数是线性空间上的范数,并以该范数的最大值定义势能判据,推导出势能判据与子结构主模态截断数量之间的关系,据此提出了一种基于势能判据的子结构主模态截断准则——势能判据截断准则,为约束模态综合法的应用提供了便利条件;
(3)针对二维模型,利用约束模态综合法,根据结构存在局部塑性区域的特点,提出了线性-非线性混合的约束模态综合法。该方法的基本思路是:对于荷载作用下整体体系中不易进入非线性阶段的部件,将其划分为线性子结构,而将体系中易进入非线性阶段、产生塑性变形的局部部件独立划分为非线性子结构,通过坐标变换来缩减线性子结构的自由度,最终与物理坐标下的非线性子结构进行综合求解。二维地基土-高层建筑非线性地震响应分析表明线性-非线性混合的约束模态综合法是有效的,并且计算结果具有较高的求解精度和计算效率。
(4)将线性-非线性混合的约束模态综合法推广至三维模型的动力分析问题中,给出了当非线性子结构与多个线性子结构存在边界耦合情况的计算方法。针对两种不同的整体土域边界条件分别进行了多组地震动激励作用下的动力时程分析,算例结果验证了方法的精确性与有效性。同时针对非线性土体区域范围的多种不同取值进行了多组数值试验,数值试验的结果进一步说明了当对分析具有一定经验时,采用线性-非线性混合的约束模态综合法能够在更大程度上提高计算效率;
(5)为了便于在专业设计软件中考虑土-结相互作用的影响,在线性-非线性混合的约束模态综合法以及分枝模态法的基础上,提出了适用于非线性土-结构相互作用体系的分枝模态与约束模态的混合方法。在该混合方法的基础上进一步提出了混合二步分析法。分析结果表明,该混合二步分析法在实现上部结构和地基土“分开”计算的同时,还能够考虑结构与地基土的材料非线性特性,有利于采用专业设计软件仅通过对上部结构进行分析来考虑土-结构相互作用的影响,为实际工程计算中引入土-结构相互作用的影响提供了便利的条件。
Multi-story building is gradually adopted since it has advantages such as saving land and making efficient use of architectural space. As our country is sited at earthquake-prone area, seismic analysis of multi-story building has been paid much more attention. Structural earthquake damage is closely related to ground condition, so it’s necessary to introduce the effect of soil-structure interaction. However, high cost of calculation, complicated analysis process, difficulties of engineering application are key problems while coping with the problem. Therefore, searching for efficient and convenient methods has theoretical significance and engineering value. Response to the above problems, this thesis has done some research. The following innovative work and achievements are included:
(1) Constrained mode synthesis (CMS) method is discussed and applied to a soil-multistory building interaction system. Method of forming the damping matrix by CMS method in a non-proportional damped system is presented, and the reduction method of degree of freedom (DOF) on the interface is also introduced. Result shows that the method is completely applicable for modal analysis and elastic time history analysis of soil-multistory building interaction system.
(2) Based on constrained mode synthesis method, a linear space consists of displacement vectors calculated by different mode cut-off numbers is defined. A function is also defined and verified to be a norm of this linear space mathematically. Then adopt the maximum value of that norm as the potential energy criterion. The relationship between potential energy criterion and mode cut-off number is derived. Consequently, the mode cut-off criterion based on potential energy criterion is proposed. It provides convenience for using constrained mode synthesis method.
(3) Based on the characteristic that structures exist local plastic regions, the mixed linear-nonlinear CMS method was presented. The basic idea is to define the component which is hard to get into nonlinear stage in the system as linear substructure while others as nonlinear substructure. DOF of linear substructures is reduced and will synthesized with nonlinear substructures, subsequently solve the mixed equation and obtain the dynamic response. In addition, result of nonlinear seismic response analysis of 2-dimensional soil-multistory buildings interaction system shows that the proposed method is effective and accurate.
(4) Expand the mixed linear-nonlinear CMS method to dynamic analysis of 3-dimensional model. For 3-dimensional dynamic analysis, the way of using the mixed linear-nonlinear CMS method is discussed when non-linear substructure is coupled with several linear substructures. Furthermore, the proposed method is used to solve the 3-dimensional soil-multistory buildings interaction system dynamic problem and several dynamic analysis has been carried out according to two kinds of soil boundary conditions by different seismic excitations. The results indicate that the proposed method is accurate and effective. In addition, the nonlinear soil region scale is studied by several numerical experiments. The results show that this method could be more effective when more experience is involved.
(5) To introduce the effect of nonlinear soil-structure interaction easily, based on the mixed linear-nonlinear constrained mode synthesis method and branch mode synthesis method, the mixed branch mode and constrained mode method is proposed. Furthermore, a mixed two-step method is also proposed on the basis of the mixed method. Results of seismic analysis of soil-multi-story frame interaction system indicate that the mixed two-step method could analyze superstructure and soil separately with the consideration of material nonlinearity. It is also beneficial to consider the effect of soil-structure interaction by only analyzing the superstructure model while using the professional design programs.
引文
[1] Georges Binder. One hundred one of the world’s tallest buildings[M]. Victoria: Publishing.Group Pty Ltd, 2006.
[2]周坚,伍孝波.复杂高层建筑结构计算[M].北京:中国电力出版社, 2008.
[3]吕西林.复杂高层建筑结构抗震理论与应用[M].北京:科学出版社, 2007.
[4]汪加武.考虑土-结构相互作用高层框架结构平面非线性抗震分析: [硕士学位论文],湖南:湖南大学, 2004.
[5]窦立军,杨柏坡,刘光和.土-结构动力相互作用几个实际应用问题[J].世界地震工程. 1999, 15(4): 62-68.
[6] Wolf J P. Dynamic soil-structure interation[M]. NewJersey: Prentice-Hall, 1985.
[7]王开顺等.土与结构相互作用地震反应研究及实用计算[J].建筑结构学报. 1986, 7(2): 64-76.
[8] Lamb H. On the propagation of tremor over the surface of an elastic solid[J]. Philosophical Transactions of the Royal Society, Ser. 1904, 203: 1-42.
[9] Lysmer J, Richart F E Jr. Dynamic response of footings to vertical loading[J]. Journal of Soil and Mechanic Found Division ASCE, 1966, 92(1): 65-91.
[10] Bycroft G N. Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum[J]. Philosophical Transactions of the Royal Society, Ser. 248: 327-368.
[11] Arnod R N, Bycroft G N, Warburton G B. Forced vibrations of body on an infinite elastic solid[J]. Journal of Applied Mechanics, Trans. ASME, 1955, 77: 391-400.
[12] Luco J E, W estman R A. Dynamic response of circular footings[J]. Journal of Engineering and Mechanic Division, ASCE, 1971, 97: 1381-1395.
[13] Lysmer J, Richart F E T. Dynamic response of footings to vertical loading[J]. Journal of Soil Mechanic Division, ASCE, 1966, 92(1): 65-91.
[14] Wolf J P, Somanini. Approximate dynamic model of embedded foundation in time domain[J]. Earthquake Engineering and Structural Dynamics. 1986, 14(5): 683-703.
[15]王泽明.土-结构动力相互作用对结构控制的影响: [硕士学位论文],天津:天津大学, 2004.
[16]尹华伟.土-结构动力相互作用的计算方法研究: [博士学位论文],湖南:湖南大学, 2005.
[17]陈国兴.土体-结构体系地震性能研究[J].哈尔滨建筑工程学院学报. 1994, 27(5): 11-18.
[18]石磊.高层建筑土-结构相互作用地震反应分析方法: [硕士学位论文],哈尔滨:中国地震局工程力学研究所, 2005.
[19]肖晓春,林皋等.桩-土-结构动力相互作用的分析模型与方法[J].世界地震工程, 2002, 18(4): 123-130.
[20]侯兴民,廖振鹏.基础动力刚度的精确数值解及集中参数模型[J].地震工程与工程振动. 2001, 21(4): 24-28.
[21]熊建国.土-结构动力相互作用问题的新进展(I)[J].世界地震工程. 1992, 8(3): 22-29.
[22]孙树民.土-结构动力相互作用研究进展[J].中国海洋平台. 2001, 16(5,6): 31-37.
[23]杜修力,赵建锋,韩强.精度可控地基阻抗力的一种时域差分计算方法[J].力学学报. 2008, 40(1): 59-66.
[24] Lymser J, Kuhlemeyer R L. Finite dynamic model for infinite media[J]. Journal of Engineering Mechanic, ASCE, 1969, 95(EM4): 859-877.
[25]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.
[26] Lysmer J, Wass G. Shear wave in plane infinite structures[J]. Journal of Engineering Mechanic Division, ASCE, 1972, 98(EM1): 85-105.
[27] Smith W D. A nonreflecting plane boundary for wave propagation problems[J]. Journal of Computational Physics, 1974, 15: 492-503.
[28] Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations[J]. Bulletin of the Seismological Society of America. 67(6): 1529-1540.
[29]廖振鹏.工程波动理论导论[M].北京:北京科学出版社, 2002, 116-120.
[30]廖振鹏.法向透射边界条件[J].中国科学(E辑). 1996, 26(2): 185-192.
[31]廖振鹏,黄孔亮,杨柏坡等.暂态波透射边界[J].中国科学辑(A辑). 1984, 27(6): 556-564.
[32]杨柏坡,廖振鹏.结构-土相互作用有限元解法及改造通用程序的初步结果[J].地震工程与工程振动. 1986, 6(4): 10-20.
[33]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, 35(8): 874-882.
[34]景立平,廖振鹏.透射边界真实反射系数的研究[J].地震工程与工程振动. 1997, 17(2): 21-26.
[35]赵建锋.考虑土-结构动力相互作用和多点输入的桥梁非线性地震响应分析: [博士学位论文],北京:北京工业大学, 2007.
[36] AM Halabian, Naggar M H. Effect of non-linear soil-structure interaction on seismic response of tall slender structures[J]. Soil Dynamic and Earthquake Engineering. 2002, 22: 639-658.
[37]杜修力,赵建锋.考虑土-结构相互作用效应的结构地震响应时域子结构分析法[J].北京工业大学学报. 2007, 33(5): 539-545.
[38] Kutanis M, Elmas M. Non-linear seismic soil-structure interaction analysis based on the substructure method in the time domain[J]. Turkish Journal of Engineering and Environmental Science. 2001, 25: 617-626.
[39] Zhang X, Wegner J L, Haddow J B. Three-dimensional dynamic soil-structure interaction analysis in the time domain[J]. Earthquake Engineering & Structural Dynamics. 1999, 28: 1501-1524.
[40] Bernal D. A dynamic stiffness formulation for the analysis of secondary systems[J]. Earthquake Engineering & Structural Dynamics. 1999, 28: 1295-1308.
[41] Bernal D. A Youssef. A hybrid time frequency domain formulation for non-linear soil structure interaction[J]. Earthquake Engineering & Structural Dynamics. 1998, 27(7): 673-685.
[42] Darbre G R. Application of the hybrid frequency-time-domain procedure to the soil-structure interaction analysis of a shear building with multiple nonlinearities[J]. Proceedings of the 10th World Conference Earthquake Engineering, Madrid, Span. 1992, 442-545.
[43] Darbre G R.Seismic analysis of non-linearly base-isolated soil-structure interacting reactor building by way of the hybrid-frequency-time-domain procedure[J]. Earthquake Engineering & Structural Dynamics. 1990, 19: 725-738.
[44]楼梦麟.结构动力分析的子结构方法[M].上海:同济大学出版社, 1997.
[45]林皋.土-结构相互作用对高层建筑非线性地震反应的影响[J].土木程学报. 1993, 26(4): 1-13.
[46] Jean W Y, Lin T W, Penzien J. System parameters of soil foundations for time domain dynamic analysis[J]. Earthquake Engineering & Structural Dynamics. 1990, 19(4): 541-553.
[47] Penzien J, Scheffey C F, Parmelee R A, et al. Seismic analysis of bridges on long piles[J]. Engineering Mechanic Division, ASCE, 1964, 90(EM3): 223-253.
[48]王有为,王开顺.建筑物-桩-土相互作用地震反应分析的研究[J].建筑结构学报. 1985, 6(5): 64-73.
[49]李永梅,孙国富,王松涛等.桩-土-杆系结构动力相互作用[J].建筑结构学报. 2002, 23(1): 75-81.
[50]刘瑞岩.结构振动模态综合技术[J].国防科学技术大学工学学报, 1979, 2(4): 62-82.
[51] Yin B S, Wang W L, Jin Y Q. The Application of Component Mode Synthesis for the Dynamic Analysis of Complex Structures Using ADINA[J]. Computers & Structures, 1997, 64(5/6): 931-938.
[52] Wolf J P. Spring-dashpot-mass models for foundation vibrations[J]. Earthquake Engineering and Structural Dynamics. 1997, 26: 931-949.
[53] Hurty W C. Vibrations of Structural Systems by Component Mode Synthesis[J]. Journal of the Engineering Mechanics Divion, ASCE, 1960, 86: 51-59.
[54] Gladwell G M L. Branch Mode Anslysis of Vibrating Systems[J]. Sound Vibration. 1964, 1: 41-59.
[55] Hurty W C. Dynamic Analysis of Structural Systems Using Component Mode [J]. AAIA Journal. 1964, 3(4): 678-685.
[56] Craig R R Jr, Bampton M C C. Coupling of Structures for Dynamic Analyses[J]. AAIA Journal. 1968, 6(7): 1313-1319.
[57] Hou Shou Nien. Review of Modal Synthesis Techniques and A New Approach[J]. Shock and Vibration Bulletin. 1969, 40: 25-30.
[58] Takewaki I, Uetani K. Inverse component-mode synthesis method for damped large structural systems[J]. Computers & Structures. 2000, 78(1-3): 415-423.
[59]白建方.复杂场地土层地震反应分析的并行有限元方法: [博士学位论文],上海:同济大学, 2007.
[60] Tran D M. Dynamic Analysis of Structural Systems Using Component Mode[J]. Computers and Structures. 2001, 79: 209-222.
[61] Craig R R Jr. A Review of Time-domain and Frequency-domain Component Mode Synthesis Method[J]. Modal Analysis. 1987, 2: 59-72.
[62] Bourquin F. Component mode synthesis and eigenvalues of second-order operators: discretization and algorithm[J]. Mathematical Modeling and Numerical Analysis. 1992, 26(3):385-423.
[63] Bucher C U A. A Modal Synthesis Method Employing Physical Coordinates, Free Component Modes and Residual Flexibilities[J]. Computers and structures, 1986, 22(4): 559-564.
[64] Hintz R M. Analytical methods in component modal synthesis[J]. AIAA Journal. 1975, 13(8): 1007-1016.
[65] Goldman R L. Vibration analysis by dynamic partitioning[J]. AIAA Journal. 1969, 7(6): 1152-1154.
[66] Rubin S. Improved component-mode representation for structural dynamic analysis[J]. AIAA Journal. 1975, 13(8): 995-1006.
[67] MacNeal R H. A hybrid method of component mode synthesis[J]. Computers and Structures. 1971, 1(4): 581-601.
[68] Craig R R Jr. Substructure Method in Vibration[J]. Transaction of the ASME. 1995, 117: 207-213.
[69]林瑾,盛宏玉.高层框架剪力墙结构与桩-土共同作用的时程响应分析[J].合肥工业大学学报(自然科学版). 2006, 29(8): 1013-1017.
[70]李忠献,何玉傲.非经典阻尼结构动力分析模态综合法论述[J].工程力学. 1992, 9(1): 51-58.
[71] Ray W Clough, Soheil Mojtatedi. Earthquake Response Anaysis Considering Non-proportional Damping[J]. Earthquake Engineering and Structural Dynamic. 1976, 4: 489-496.
[72] Morgan J A, Pierre C, Hulbert G M. Baseband methods of component mode synthesis for non-proportionally damped systems[J]. Mechanical Systems and Signal Processing. 2003, 17(3): 589-598.
[73] Craig R R Jr, Chang C J. A Review of Substructure Coupling Methods for Dynamic Analysis[J]. Advances in Engineering Science. 1976, 2: 393-408.
[74] Anil K Chopra. Dynamics of Structures: theory and applications to earthquake engineering, Second edition[M]. Berkeley: University of California. 2001, 454-464.
[75] Kyung R G, Shin H C. Dynamic Analysis of Structures Using Constrained Component Mode Synthesis[J]. AIAA Modeling and Simulation Technologies Conference and Exhibit. 2002 Aug 5-8, California, Monterey:AIAA-2002-4797.
[76] Wamsler M. On the Selection of the Mode Cut-off Number in Component Mode Reduction[J]. Engineering with Computers. 2009, 25: 139-146.
[77]丁平,顾彦.子结构模态综合在汽车振动噪声分析的应用[J].上海汽车. 2007, 11: 22-24.
[78]张美艳,韩平畴.结构动力重分析的子结构有理逼近[J].计算力学学报. 2008, 25(6): 878-881.
[79] Wang X Y, Mills J K. Dynamic Modeling of a Flexible-link Planar Parallel Platform Using a Substructuring Approach[J]. Mechanism and Machine Theory. 2006, 4: 671-687.
[80]管根红,陈常顺,高树滋.基于系统响应的模态截断方法的研究[J].南京理工大学学报. 2000, 24(6): 532-535.
[81]田育民.复杂结构模态分析中的截断准则[J].强度与环境. 1994, 2: 18-21.
[82]宋修广,钟原,刘西利.基于能量范数的模态密集型系统的模态截断[J].山东大学学报. 2002, 32(4): 321-324.
[83]谢能刚,郭兴文,王德信.结构振动模态截断的能量判据[J].振动工程学报. 2003, 16(3): 302-305.
[84]谢能刚,赵雷,方浩.基于能量法的强夯频域分析[J].岩石力学与工程学报. 2006, 25(1): 3224-3228.
[85]谢能刚,王德信.高拱坝地震响应分析中的能量法[J].土木工程学报. 2003, 36(6): 85-87.
[86]谢能刚,王德信,孙林松.能量函数在高拱坝动力优化设计中的应用[J].应用力学学报. 2002, 19(2): 107-109.
[87]熊洪允,曾绍标,毛云英.应用数学基础[M].天津:天津大学出版社, 2004.
[88]同济大学应用数学系.高等数学[M].高等教育出版社. 2002.
[89]路观平,王晓泉,王雨苗.模态综合的交叉子结构方法[J].振动工程学报. 2002, 15(3): 300-304.
[90] Pan L J, Zhang B M. A New Method for the Determination of Damping in Cocured Composite Laminates with Embedded Viscoelastic Layer[J]. Journal of Sound and Vibration. 2009, 319: 822-831.
[91]宫晓春,曹登庆.含参数多自由度非线性系统的降维方法研究[J].动力学与控制学报. 2009, 7(2): 129-135.
[92]尉飞,郑钢铁.利用POD方法的固定界面模态综合技术[J].振动工程学报.2008, 21(4): 365-370.
[93]白建方,楼梦麟.基于动力子结构方法的场地地震反应分析方法[J].震灾防御技术. 2008, 3(2): 145-154.
[94]姜忻良,王菲.基于势能判据的约束模态综合法截断准则[J].振动与冲击.已录用待发表.
[95]陈国兴,庄海洋,程绍革等.土-地铁隧道动力相互作用的大型振动台试验:试验方案设计[J].地震工程与工程振动. 2006, 26(6): 178-183.
[96]姜忻良,王菲.线性-非线性混合的约束模态综合法及实践[J].天津大学学报.已录用待发表.
[97] Wolf J P. Spring-dashpot-mass models for foundation vibrations[J]. Earthquake Engineering and Structural Dynamics. 1997, 26: 931-949.
[98]姜忻良,严士超.分枝模态二步分析法及其在液体-结构-桩土体系中的应用[J].振动工程学报. 1994, 7(4): 346-350.
[99]姜忻良,严士超,丁学成.筒体结构-桩-土相互作用的分枝模态-二步分析法[J].天津大学学报. 1995, 6: 796-801.
[100]王文亮,杜作润.结构振动与动态子结构方法[M].上海:复旦大学出版社. 1985: 229-258.