筏板基础无网格计算方法及其在考虑上部结构共同作用分析中的应用
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摘要
无网格方法是近年来迅速发展起来的一类新型数值计算方法,它们不借助单元网格而是基于离散结点动态构造近似插值函数,与传统的有限元方法有着显著的区别,克服了网格生成、网格畸变和网格移动引起的问题并为工程问题提供了一种新的有效分析方法,受到了国际计算力学界和工程界的高度重视。
本文基于国内外目前筏板基础与地基及上部结构共同工作课题及无网格数值分析方法研究发展的趋势,在充分借鉴并发挥前人研究的基础上,研究了弹性地基板的无网格计算分析方法,并将其应用于筏板基础与地基及上部结构共同工作的数值计算分析之中。
本文的研究成果及创新点主要如下:
①推导了无网格重构核粒子法(RKPM)、无单元伽辽金法(EFGM)、自然单元法(NEM)三种无网格法的形函数在二维域内的一阶、二阶导函数,并将其应用于板弯曲C1(即要求域内的导数连续)问题,建立了Winkler地基上Kirchhoff薄板的无网格法分析理论。其中,首次求出了NEM无网格法的形函数在二维域内的二阶导函数;首次建立了Winkler地基上Kirchhoff薄板的RKPM及NEM无网格法分析理论。
②在Winkler地基上Kirchhoff薄板无网格法分析理论的基础上,进一步建立了双参数地基上Kirchhoff薄板无网格法分析理论,拓展了弹性地基薄板弯曲无网格法的地基适用范围,使该理论更符合工程实际情况。其中,首次建立了双参数地基上Kirchhoff薄板的RKPM及NEM无网格法分析理论。
③建立了Winkler地基及双参数地基上Mindlin中厚板的无网格法分析理论,将EFGM法、RKPM法、NEM法这三种无网格法应用于Mindlin中厚板弯曲问题,推动了弹性地基上中厚板计算理论的发展。该理论同时适用于弹性地基上薄、中厚、厚板的计算,基于无网格法节点布置灵活的特性,可推广应用于任意平面形状的地基板的求解。其中,首次建立了Winkler地基上Mindlin中厚板的RKPM、NEM无网格法分析理论;首次建立了双参数地基上Mindlin中厚板的RKPM、EFGM及NEM无网格法分析理论。
④首次将上部框架结构的子结构有限元法与筏板基础的无网格法(包括EFGM、RKPM、NEM三种无网格法)耦合起来进行计算分析,从而建立了一种新的高层建筑框架结构与筏板基础与地基的共同作用分析方法,通过算例分析及与商业有限元软件ANSYS计算结果的比较,表明该方法是有效可行的。
⑤在上部结构中引入剪力墙及楼板单元,将其加入到上部结构有限元子结构中,再与筏板基础的无网格法耦合起来进行计算分析,从而使该共同作用新方法能对工程实际中高层建筑的不同上部结构(如框架-剪力墙结构、筒体结构、框架-筒体结构)与筏板基础、地基共同作用进行计算分析,通过算例分析及与商业有限元软件ANSYS计算结果的比较,表明该方法是有效可行的。
⑥针对上述各种计算理论及分析内容,自行编制了相应的面向对象计算程序PIASRFS-2007,程序用C++语言在VC++平台中编制,采用该程序可以采用无网格法对筏板基础进行计算分析,并能对不同平面形状、不同厚度的筏板基础与Winkler、双参数弹性地基及高层建筑的不同上部结构进行三者的共同作用计算分析,该程序为高层建筑筏板基础工程实践提供了一种新型有效的分析手段。通过程序计算可以得出工程上关心的考虑与上部结构、地基共同作用的筏板基础的挠度(地基的沉降)、筏板基础内力、上部结构(包括上部各层梁、柱、剪力墙)内力等结构设计所需的指标,可为相关的具体工程实践提供指导及依据。
Meshless method is a new numerical computation method that is developed rapidly in recent years. Without element mesh and based on the dispersed nodes to form approximate interpolative function dynamically, meshless method has distinct difference with traditional finite element method. Meshless method conquers the problems caused by mesh generation, mesh aberration and mesh move. With provides a new effective means to engineering problem, meshless method obtain highly recognition in international compute mechanics domain and engineering field.
Based on the developing trends of the meshless numerical analytical method and the interaction research of raft foundation with soil and superstructure, meshless computation methods for elastic foundation plate are researched by using the relative works in existence for reference adequately. And this elastic foundation plate meshless method computation theory is used in the interaction numerical analysis of raft foundation with soil and superstructure.
The main work and innovative achievements are as follows:
①The 1st and 2nd derivatives to the shape functions of reproducing kernel particle method (RKPM) and natural element method (NEM) are deduced in two-dimensional domain. With the application of above derivatives to plate bending C1 problem (Which require shape function has continuous derivative in its definition domain), meshless method analysis theory is built for Kirchhoff thin plate bending on Winkler foundation and thus promote the development of elastic foundation thin plate theory. Among these work, 2nd derivative to the shape functions of NEM and the RKPM, NEM meshless method of Kirchhoff thin plate bending on Winkler foundation are innovative.
②Based on the meshless method analysis theory of Kirchhoff thin plate bending on Winkler foundation, meshless method analysis theory of Kirchhoff thin plate bending on two-parameter foundation is developed. This broaden the foundation application area of elastic foundation thin plate bending analysis meshless method and make the theory accord with the practice much more. Among these work, RKPM, NEM meshless method of Kirchhoff thin plate bending on two-parameter soil foundation are innovative.
③Meshless method analysis theory of Mindlin medium-thick plate bending on Winkler and two-parameter foundation is built. Element-free Galerkin method (EFGM), reproducing kernel particle method (RKPM), natural element method (NEM) are used to solve Mindlin medium-thick plate bending problem with the above theory and thus promote the development of elastic foundation medium-thick plate theory. The theory can also be used in the computation of thin, medium-thick and thick plate in elastic foundation. Based on the agility property of node disposal in meshless method, the theory can be used in the bending problem of foundation plate with arbitrary plane shape. Among these work, RKPM, NEM meshless method of Mindlin thick plate bending on Winkler foundation and RKPM, EFGM, NEM meshless method of Mindlin thick plate bending on two-parameter foundation are innovative.
④By coupled the sub-structure finite element method for frame-superstructure and the meshless method (Which include EFGM, RKPM, NEM) for raft foundation, a new method is built for the interaction analysis of high-rise frame superstructure with raft foundation and soil. With the example computation analysis and comparison with ANSYS finite element soft computation result, the method is proved to be effective and feasible.
⑤By couple the finite element sub-structure method for superstructure that used shear-wall and floor-slab element and the meshless method for foundation plate, a new analysis method for interaction analysis of high-rise frame and shear-wall superstructure with raft foundation and soil is built. The method can be used to analysis the interaction of different superstructure (Such as frame and shear-wall structure, tube structure, frame and tube structure etc.) with raft foundation and soil. With the example computation analysis and comparison with ANSYS finite element soft computation result, the method is proved to be effective and feasible.
⑥Pointed to the various computation theory and analysis content, computation program PIASRFS-2007 is devised with C++ language in VC++ platform. Raft foundation can be analyzed by this program. And interaction of raft foundation in different plane shape and different thickness with soil that simulated by Winker or two-parameter soil model and high-rise building superstructure can be computed and analyzed. The program provides a new and effective analysis tool for the practice of high-rise building raft foundation engineering. By the computation of program, data which concerned in engineering such as deflection of raft foundation (soil settlement), internal force of raft foundation, internal force of superstructure (Which include beam, columns and shear-wall) and the other useful data for structure design can be obtained. And this can provide guidance and advice for the relative engineering practice.
本文基于国内外目前筏板基础与地基及上部结构共同工作课题及无网格数值分析方法研究发展的趋势,在充分借鉴并发挥前人研究的基础上,研究了弹性地基板的无网格计算分析方法,并将其应用于筏板基础与地基及上部结构共同工作的数值计算分析之中。
本文的研究成果及创新点主要如下:
①推导了无网格重构核粒子法(RKPM)、无单元伽辽金法(EFGM)、自然单元法(NEM)三种无网格法的形函数在二维域内的一阶、二阶导函数,并将其应用于板弯曲C1(即要求域内的导数连续)问题,建立了Winkler地基上Kirchhoff薄板的无网格法分析理论。其中,首次求出了NEM无网格法的形函数在二维域内的二阶导函数;首次建立了Winkler地基上Kirchhoff薄板的RKPM及NEM无网格法分析理论。
②在Winkler地基上Kirchhoff薄板无网格法分析理论的基础上,进一步建立了双参数地基上Kirchhoff薄板无网格法分析理论,拓展了弹性地基薄板弯曲无网格法的地基适用范围,使该理论更符合工程实际情况。其中,首次建立了双参数地基上Kirchhoff薄板的RKPM及NEM无网格法分析理论。
③建立了Winkler地基及双参数地基上Mindlin中厚板的无网格法分析理论,将EFGM法、RKPM法、NEM法这三种无网格法应用于Mindlin中厚板弯曲问题,推动了弹性地基上中厚板计算理论的发展。该理论同时适用于弹性地基上薄、中厚、厚板的计算,基于无网格法节点布置灵活的特性,可推广应用于任意平面形状的地基板的求解。其中,首次建立了Winkler地基上Mindlin中厚板的RKPM、NEM无网格法分析理论;首次建立了双参数地基上Mindlin中厚板的RKPM、EFGM及NEM无网格法分析理论。
④首次将上部框架结构的子结构有限元法与筏板基础的无网格法(包括EFGM、RKPM、NEM三种无网格法)耦合起来进行计算分析,从而建立了一种新的高层建筑框架结构与筏板基础与地基的共同作用分析方法,通过算例分析及与商业有限元软件ANSYS计算结果的比较,表明该方法是有效可行的。
⑤在上部结构中引入剪力墙及楼板单元,将其加入到上部结构有限元子结构中,再与筏板基础的无网格法耦合起来进行计算分析,从而使该共同作用新方法能对工程实际中高层建筑的不同上部结构(如框架-剪力墙结构、筒体结构、框架-筒体结构)与筏板基础、地基共同作用进行计算分析,通过算例分析及与商业有限元软件ANSYS计算结果的比较,表明该方法是有效可行的。
⑥针对上述各种计算理论及分析内容,自行编制了相应的面向对象计算程序PIASRFS-2007,程序用C++语言在VC++平台中编制,采用该程序可以采用无网格法对筏板基础进行计算分析,并能对不同平面形状、不同厚度的筏板基础与Winkler、双参数弹性地基及高层建筑的不同上部结构进行三者的共同作用计算分析,该程序为高层建筑筏板基础工程实践提供了一种新型有效的分析手段。通过程序计算可以得出工程上关心的考虑与上部结构、地基共同作用的筏板基础的挠度(地基的沉降)、筏板基础内力、上部结构(包括上部各层梁、柱、剪力墙)内力等结构设计所需的指标,可为相关的具体工程实践提供指导及依据。
Meshless method is a new numerical computation method that is developed rapidly in recent years. Without element mesh and based on the dispersed nodes to form approximate interpolative function dynamically, meshless method has distinct difference with traditional finite element method. Meshless method conquers the problems caused by mesh generation, mesh aberration and mesh move. With provides a new effective means to engineering problem, meshless method obtain highly recognition in international compute mechanics domain and engineering field.
Based on the developing trends of the meshless numerical analytical method and the interaction research of raft foundation with soil and superstructure, meshless computation methods for elastic foundation plate are researched by using the relative works in existence for reference adequately. And this elastic foundation plate meshless method computation theory is used in the interaction numerical analysis of raft foundation with soil and superstructure.
The main work and innovative achievements are as follows:
①The 1st and 2nd derivatives to the shape functions of reproducing kernel particle method (RKPM) and natural element method (NEM) are deduced in two-dimensional domain. With the application of above derivatives to plate bending C1 problem (Which require shape function has continuous derivative in its definition domain), meshless method analysis theory is built for Kirchhoff thin plate bending on Winkler foundation and thus promote the development of elastic foundation thin plate theory. Among these work, 2nd derivative to the shape functions of NEM and the RKPM, NEM meshless method of Kirchhoff thin plate bending on Winkler foundation are innovative.
②Based on the meshless method analysis theory of Kirchhoff thin plate bending on Winkler foundation, meshless method analysis theory of Kirchhoff thin plate bending on two-parameter foundation is developed. This broaden the foundation application area of elastic foundation thin plate bending analysis meshless method and make the theory accord with the practice much more. Among these work, RKPM, NEM meshless method of Kirchhoff thin plate bending on two-parameter soil foundation are innovative.
③Meshless method analysis theory of Mindlin medium-thick plate bending on Winkler and two-parameter foundation is built. Element-free Galerkin method (EFGM), reproducing kernel particle method (RKPM), natural element method (NEM) are used to solve Mindlin medium-thick plate bending problem with the above theory and thus promote the development of elastic foundation medium-thick plate theory. The theory can also be used in the computation of thin, medium-thick and thick plate in elastic foundation. Based on the agility property of node disposal in meshless method, the theory can be used in the bending problem of foundation plate with arbitrary plane shape. Among these work, RKPM, NEM meshless method of Mindlin thick plate bending on Winkler foundation and RKPM, EFGM, NEM meshless method of Mindlin thick plate bending on two-parameter foundation are innovative.
④By coupled the sub-structure finite element method for frame-superstructure and the meshless method (Which include EFGM, RKPM, NEM) for raft foundation, a new method is built for the interaction analysis of high-rise frame superstructure with raft foundation and soil. With the example computation analysis and comparison with ANSYS finite element soft computation result, the method is proved to be effective and feasible.
⑤By couple the finite element sub-structure method for superstructure that used shear-wall and floor-slab element and the meshless method for foundation plate, a new analysis method for interaction analysis of high-rise frame and shear-wall superstructure with raft foundation and soil is built. The method can be used to analysis the interaction of different superstructure (Such as frame and shear-wall structure, tube structure, frame and tube structure etc.) with raft foundation and soil. With the example computation analysis and comparison with ANSYS finite element soft computation result, the method is proved to be effective and feasible.
⑥Pointed to the various computation theory and analysis content, computation program PIASRFS-2007 is devised with C++ language in VC++ platform. Raft foundation can be analyzed by this program. And interaction of raft foundation in different plane shape and different thickness with soil that simulated by Winker or two-parameter soil model and high-rise building superstructure can be computed and analyzed. The program provides a new and effective analysis tool for the practice of high-rise building raft foundation engineering. By the computation of program, data which concerned in engineering such as deflection of raft foundation (soil settlement), internal force of raft foundation, internal force of superstructure (Which include beam, columns and shear-wall) and the other useful data for structure design can be obtained. And this can provide guidance and advice for the relative engineering practice.
引文
[1] 徐至钧,陈祥福.超高层建筑结构设计与施工.北京:机械工业出版社,2007
[2] 宰金珉,宰金璋.高层建筑基础分析与设计——土与结构物共同作用的理论与应用.北京:中国建筑工业出版社,2001
[3] 张雄,刘岩.无网格法.北京:清华大学出版社,2004
[4] Belytschko T, Krongauz Y, Organ D. Meshless methods: An overview and recent development. Comput. Methods Appl. Mech. Engrg. ,1996,139:3-47
[5] 盂闻远,卓家寿.无网格的崛起与进展——一种新兴的数值方法评述.河海大学学报,1999,27(力学专辑):51-58
[6] 曹国金,姜弘道.无单元法研究和应用现状及动态.力学进展,2002,32(4):526-534
[7] 生跃,黄义.双参数弹性地基上自由矩形板.应用数学和力学,1987,8(4)
[8] 熊渊博.Kirchhoff 板问题的无网格局部 Petrov-Galerkin 方法研究[博士学位论文].长沙:湖南大学,2005
[9] 蔡长忠.弹性地基自由边圆形厚板在偏心集中力作用下弯曲问题的 Fourier 级数解.工程力学,1986,(4):27-39
[10] 石小平,姚祖康.Pasternak 基础上四边矩形厚板的解.同济大学学报,1989,17(2):173-184
[11] 宋启根,林洋,徐培.双参数地基 Reissner 板局部荷载解.岩土工程学报,1993,15(5):48-58
[12] 曲庆璋,梁兴复.不同支承条件矩形中厚板的精确解.上海力学,1997,18(1)
[13] J.T.Katsikadelis. The Analysis of Plates on Elastic Foundation by the Boundary Integral Equation Method. Thesis Presented to the Polytechnic Institute of New York, 1982
[14] J.T.Katsikadelis, A.E.Armenakas. Analysis of Clamped Plates on Elastic Foundation by the Boundary Integeral Equation Method. Journal of Applied Mechanics, 1984, Vol.51
[15] J.T.Katsikadelis and A.E.Armenakas,Plates on Elastic Foundation by BIE method. Journal of Engineering Mechanics, 1984,110(7)
[16] J.T.Katsikadelis and L.F.Kallivokas, Clamped Plates on Pasternaktype Elastic Foundation by the Boundary Element Method. Journal of Applied Mechanics, 1986, Vol.53
[17] J.Puttonen and P.Varpasuo, Boundary Element Analysis of a Plate on Elastic Foundations. Int .J.Numerical Methods in Engineering, 1986, Vol.23:287-303
[18] G.Bezine. A New Boundary Element Method for Bending of Plates on Elastic Foundations. Int.J.Solids Structures, 1988, 24(6):557-565
[19] E.J.Sapountzakis, J.T.Katsikadelis. Boundary Element Solution for Plates of VaribleThickness. Journal of Engineering Mechanics, 1991, 117(6)
[20] 邓安福,李正良.双参数地基上 Reissner 板弯曲问题的基本解.结构工程学报,1991,(3):244-249
[21] 邓安福,李正良.弹性地基上 Reissner 板的基本解.固体力学学报,1993,14(1)
[22] 李正良,邓安福.双参数地基上板弯曲问题的边界积分方程.应用数学和力学,1992,13(7):633-643
[23] 李正良,干腾君,邓安福.双参数弹性地基板的边界元法.重庆建筑工程学院学报,1995,17(1):1-7
[24] 江隆植等.纵横荷载共同作用下基础板弯曲问题样条边界元分析.上海力学,1990, (2):70-76
[25] 干腾君.空间框架—筏基—土共同工作的有限元—边界元耦合方法[硕士学位论文].重庆: 重庆建筑工程学院,1993
[26] Cheung Y. K., Zienkiewize O. C. Plates and tanks on elastic foundation – an application of finite element method. Int. J. Solids and Struc, 1965, (1):451-461
[27] Haddadin M. J. Mats and combined footings analysis by the finite element methods. J.ACI. 1971,68(2)
[28] Hain S. J., Lee I. K., Rational analysis of raft foundation. J. Geotech. Eng. Div., Proc. ASCE, 1974, 68(12)
[29] Sharma K. G., Nagpal A. K. , Grag M. K. Finite element analysis of rafts resting on elastic half space. Indian Geotechnical Journal, 1984,14(1):28-39
[30] 刘开国.地基—基础—框架体系相互作用的计算方法.建筑结构学报,1981,(5):55-72
[31] 宰金珉等.高层空间剪力墙结构与地基共同作用三维问题的双重扩大子结构有限元—有限层分析.建筑结构学报,1983,(5):57-70
[32] 朱百里,曹铭葆,魏道垛.框架结构与地基基础共同作用的数值分析——线性与非线性地基.同济大学学报,1982,(4):15-31
[33] 姚祖恩等.框架、筏基和土共同作用机理的探讨.岩土工程学报,1984,6:30-41
[34] 张季荣,蔡敏.弹性地基上片筏基础的有限单元法分析.浙江大学学报,1988,22:71-78
[35] 张祥等.双参数弹性地基上厚板的有限元边界元联合解法.岩土工程学报,1995,(1):46-52
[36] Krysl, P., Belytschko, T. Analysis of thin plates by the element-free Galerkin method. Comput. Mech., 1996,17:26-35
[37] Ouatouati,A.E., Johnson, D.A. A new approach for numerical modal analysis using the element free method. Int. J.Numer. Methods Eng., 1999, 46:1-27
[38] Liu,G.R., Chen, X. L. A mesh-free method for static and free vibration analyses of thin platesof complicated shape. J. Sound Vib., 2001, 241(5):839-855
[39] 张建辉,邓安福.无单元法在筏板基础计算中的应用.岩土工程学报, 1999,21(6):691-695
[40] 张建辉,邓安福.无单元法在弹性地基板计算中的应用.重庆建筑大学学报,1999,21(2):84-88
[41] 张伟星,庞辉.无单元法分析弹性地基板.力学与实践,2000,22(3):38-41
[42] 方电新,李卧东,王元汉.用无网格法计算平板弯曲问题.岩土力学,2001,22(3) :347-349
[43] Meyerhof,G. G. The Settlement Analysis of Building Frame. The Structural Engineer, 1947,25
[44] Meyerhof,G. G. Some Recent Foundation Research and its Application to Design, The Structure Engineer, 1953,31
[45] Chamecki. Structural Rigidty in Calculating Settlements. Jour.soil Mech.and Found. Div,ASCE,1956,82
[46] Przemienicki,J.S. Theory of Matrix Structural Analysis,1968
[47] Haddadin,M.M. Mats and Combined Footings Analysis by the Finite Element Methods. Proc, ACI, 1971, 68(12)
[48] Christian,J.T. Soil Structure-interaction for Tall Buildings. Planning and Design of Tall Buildings. Lehigh University, 1972,19
[49] King,G.J.W., Chandrasekaran. Interaction Analysis of a Rafted Multi-story Space Frame Resting on an Inhomogeneous Clay Stratum. Proc.Int.Conf.on Finite Elenent Methods in Engineering, Univ.of.N.S.w.Autralian, 1974
[50] Wardle,L.J., Fraser,R.A. Methods for Raft Foundation Design including Soil-Structure Interaction. Cooerative Project, The University of New South Wales,Australia, 1975
[51] Hooper,J.A., Wood,L.A. Foundation Analysis of a Cross-Wall Structure. Proc.Int.Conf.on Performance Big, Struc. Glasgow,1976
[52] Poulos,H.G., Davis,E.H. Pile Foundation Analysis and Design. John Wiley, New York, 1980
[53] Poulos,H.G., Soil-Structure Interaction—General Report(Preliminary). Proc.10th ICSMFE,1981
[54] 张问清,赵锡宏.逐步扩大子结构法计算高层结构刚度的基本原理.建筑结构学报,1980,(4):66-70
[55] 宰金珉,张问清,赵锡宏.平面形状为 L 形的空间剪力墙结构与不均匀的地基共同作用.岩土工程学报,1983,(2)
[56] 裴捷,张问清,赵锡宏.考虑填充墙的框架结构与地基基础共同作用的分析方法.建筑结构学报,1984,(4)
[57] 杨敏.上部结构与桩筏基础共同作用的理论与试验研究.[博士学位论文].上海:同济大学,1989
[58] 袁聚云,沈伟跃,赵锡宏.空间剪力墙结构—厚筏—桩—地基共同作用分析.上海高层建筑桩筏与桩箱基础设计理论.上海:同济大学出版社,1989
[59] 邓安福,干腾君,李正良.上部结构-筏式基础-地基共同作用分析的一种新方法.全国首届结构与介质相互作用学术会议论文集,1993
[60] 张保良,姜洪伟,赵锡宏.层状土中群桩沉降分析.上海力学,1996,(1)
[61] 中国建筑科学研究院主编.《建筑桩基技术规范》(JGJ094-94) .北京:中国建筑工业出版社,1995
[62] 叶于政,孙家乐.高层建筑箱形基础与地基和上部结构共同作用机理的初步探讨和采用弹性杆的简化计算方法.北京工业大学学报,1980,(3)
[63] 孙家乐,张雷.从高层建筑与地基基础相互作用研讨连续基础简化计算.第四届土力学基础工程学术会议论文集.北京:中国建筑工业出版社,1986
[64] 王兆清,冯伟.自然单元法研究进展.力学进展,2004,34(4):437-445
[65] 周瑞忠,周小平,吴琛.数值方法进展:从连续介质到离散粒子模型.工程力学,2005,22(增刊):228-239
[66] Gingold RA, Moraghan JJ. Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Mon. Not. Roy. Astrou. Soc., 1977, 18:375-389
[67] Liu W K, Jun S, Adee J, Belytschko T. Reproducing kernel particle methods. Int J Numer Methods Engrg, 1995, 38(10):1655-1679
[68] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. Int. J. for Num. Methods in Eng.,1994, 37:229-256
[69] Cordes LW, Moran B. Treatment of material discontinuity in the Element-free Galerkin method. Comput Meth Appl Mech Eng, 1996, 139: 3-47
[70] 庞作会,葛修润,郑宏等. 一种新的数值计算方法无网格伽辽金法. 计算力学学报,1999,18(5): 581-584
[71] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. Int J Num Meth Eng,1998,41:1215-1233
[72] Onate E, Idelsohn S, Zienkiewicz O C, Talor R L. A finite point method in computational mechanics application to convective transport and fluid flow. Int J Numer Methods Engrg, 1996, 39(22):3839-3866
[73] Duarte C A, Oden J T. Hp clouds: a h-p meshless method, Numerical Methods for Partical Differential Equations,1996,12:673-705
[74] Zhu T, Zhang J, Arluri S N. A meshless local boundary integral equation method for solving nonlinear problems. Computational Mechanics,1998,22(3):174-186
[75] Braun J, Sambridge M. A numerical method for solving partial differential equations on highly irregular evolving grids. Nature, 1995, 376: 655-660
[76] N. Sukumar and B. Moran and T. Belytschko. The natural element method in solid mechanics. 1998. International Journal for Numerical Methods in Engineering, 43(5):839-887.
[77] N. Sukumar and B. Moran and A. Yu. Semenov and V. V. Belikov. Natural neighbor Galerkin methods. International Journal for Numerical Methods in Engineering, 2001. 50(1):1-27.
[78] Sukumar N. Voronoi cell finite difference method for the diffusion operator on arbitary unstructured grids. Int J Num Meth Eng,2003,57:1-34
[79] Cueto E, Doblare M, Gracia L. Imposing essential boundary conditions in the natural element method by density-scaled α-shapes. Int J Num Meth Eng,2000,49:519-546
[80] 蔡永昌,李晓军,朱合华.基于局部 Petrov-Galerkin 过程的自然单元法及其面向对象的设计与实现. 岩石力学与工程学报,2003,22(8):1263-1268
[81] 蔡永昌,朱合华. 岩土工程数值计算中的无网格方法及其全自动布点技术. 岩土力学,2003,24(1):21-24
[82] 蔡永昌,朱合华,王建华. 基于 Voronoi 结构的无网格局部 Petrov-Galerkin 方法. 力学学报,2003,35(2):187-193
[83] 张雄,宋康祖,陆明万. 紧支试函数加权残量法. 强度与环境,2000,增刊: 58-63
[84] Zhang X, Song K Z, Lu M W, Chen Y. Imposition of essential boundary conditions by displacement constraint equations in meshless methods. Communications in Numrical Methods in Engineering, 2001, 17(3): 165-178
[85] Zhang X, Song K Z, Lu M W. Hermite type collocation with radial funcations. In: Proceedings of international conference on computational engineering & science, 2000, Los Angels. 1445-1450
[86] 刘欣,朱德懋,陆明万,张雄. 基于流形覆盖思想的无网格方法的研究. 计算力学学报,2001,18(1): 21-27
[87] 栾茂田,田荣,杨庆等. 有限覆盖无单元法在岩土类弱拉型材料接触摩擦问题中的应用.岩土工程学报,2002,24(2):137-141
[88] 张湘伟,蔡永昌. 一种改进的无单元法. 计算力学学报,2002.19(1): 26-30
[89] 秦荣. 样条无网格法. 见: 袁明武,孙树立编. 工程与科学中的计算力学,中国计算力学大会’2001 论文集,广州,2001 年 12 月 6-8 日. 北京: 北京大学出版社,2001. 327-332
[90] 何沛祥,李子然,吴长春. 无网格法与有限元的耦合及其对功能梯度材料断裂计算的应用. 中国科学技术大学学报,2001,31(6): 673-680
[91] 袁振,李子然,吴长春. 无网格法模拟复合型疲劳裂纹的扩展.工程力学,2002,19(1): 25-28
[92] 周忠瑞,周小平,缪冰. 小波基无单元法及其工程应用. 工程力学,2003,20(6): 70-74
[93] 屈智炯,土的塑性力学,成都,成都科技大学出版社, 第一版,1987
[94] 周进雄,李梅娥,张红艳,张陵. 再生核质点法研究进展,力学进展,2002,32(4)
[95] Liu W K, Jun S, Zhang Y F. Reproducing Kernel particle methods. Int J Numer Methods Engrg, 1995, 20:1081-1106
[96] Liu W K, Jun S, et al. Reproducing Kernel particle methods for structure dynamics. Int J Numer Methods Engrg, 1995, 38: 1655-1679
[97] Liu W K, Chen Y. Wavelet and multiple scale reproducing Kernel methods. Int J Numer Methods Fluids, 1995, 21: 901-931
[98] Liu W K, Chen Y, Uras R. A. Enrichment of the finite element method with reproducing Kernel particle method. In: Cory J J F, Gordon J L, eds. Current Topics in Computational Mechanics. ASME PVP, 1995, 305. 253-258
[99] 库东峰. 再生核粒子法及其在平板弯曲问题中的应用[硕士学位论文].南京:南京航空航天大学,2005
[100] 史宝军,袁明武,李君. 基于核重构思想的最小二乘配点型无网格方法. 力学学报,2003,35(6) : 697-706
[101] 史宝军,袁明武,孙树立,陈斌. 基于核重构思想的配点型无网格方法的研究——一维问题. 计算力学学报,2004,21(1) : 97-103
[102] Lu Y Y, Belytschko T, Gu L. A new implementation of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1994, 113: 397-414.
[103] 张建辉. 层状地基上桩筏基础的分析方法及其布桩优化研究[博士学位论文]. 重庆:重庆建筑大学,1999
[104] G. R. Liu. Mesh Free Methods: Moving Beyond the Finite Element Method. London:CRC Press,2002
[105] 蔡永昌,朱合华. 基于局部搜索算法的自然邻接点方法. 力学学报,2004,36(5) : 623-628.
[106] 朱怀球,吴江航. 一种基于 Voronoi Cells 的 C∞插值基函数及其在计算流体力学中的若干应用. 北京大学学报(自然科学版),2001,37(5):669-678.
[107] Green P J, Sibson R R. Computing dirichlet tessellations in the plane. The ComputerJournal,1978,21:168-173
[108] Hisamoto Hiyoshi. Study on interpolation based on Voronoi diagrams:[dissertation]. Tokyo:University of Tokyo,2000
[109] Belikov V and Semenov A. Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive generating isolines algorithm.Numerical Grid Generation in Computational Field Simulation, Proc. Of the 6th Intl. Conf. Greenwich Univ.July 1998
[110] Hisamoto Hiyoshi, Kokichi Sugihara. Two generalizations of an interpolant based Voronoi diagrams. International Journal of Shape Modeling, 1999,5(2):219-231
[111] 胡海昌. 弹性力学的变分原理及其应用. 北京:科学出版社,1987
[112] 张福范. 弹性薄板. 北京:科学出版社,1984
[113] 张建辉. 双参数地基板的无单元法. 岩土工程学报,2005,27(7):776-779
[114] 季求知,曲庆章.双参数弹性地基上四边自由矩形板问题. 青岛建筑工程学院学报,1996,17(3):85-93
[115] 王勖成,邵敏. 有限单元法基本原理和数值方法. 北京:清华大学出版社,1997.
[116] 包彦. 带裙房高层建筑与地基基础共同作用的理论应用与工程实践研究[博士学位论文].上海:同济大学,2003.12
[117] 曾祥勇,邓安福. 弹性地基上水工结构各向异性 Mindlin 底板计算分析的无单元法(EFGM).岩土力学,2006 增刊(2)
[118] 董建国,赵锡宏. 高层建筑地基基础——共同作用理论与实践. 上海:同济大学出版社,1997
[119] 黄义,何芳社. 弹性地基上的梁、板、壳. 北京:科学出版社,2005
[120] 孙卫明,杨光松,张承宗. 双参数地基上弹性厚板弯曲的一般解析解. 工程力学,1999,16(2):71-78
[121] 梁清香. 有限元与 marc 实现,机械工业出版社,第一版,2003
[122] 方世敏. 上部结构与地基基础共同工作的子结构分析法. 建筑结构学报,1980,(4)
[123] 陈希昌. 高层建筑物上部结构与基础及地基共同作用问题研究[博士学位论文]. 重庆:重庆建筑大学,1997
[124] 吴晓涵. 面向对象结构分析程序设计. 北京:科学出版社,2002,(4)
[125] 罗立平,赵锡宏. 空间框架结构——厚筏——地基共同作用分析. 上海高层建筑桩筏与桩箱基础设计理论. 上海:同济大学出版社,1989
[126] 干腾君. 考虑上部结构共同作用的筏板基础分析及其优化[博士学位论文]. 重庆:重庆大学,2001
[127] 陈卓. 上部结构、筏板、地基共同作用的面向对象有限元分析[硕士学位论文]. 重庆:重庆大学,2004,(5)
[128] A.P.S Selvadurai 著. 范文田等译. 土与基础相互作用的弹性分析. 北京:中国铁道出版社,1984
[129] 王元淳. 边界元法基础. 上海:上海交通大学出版社,1988
[130] 钱家欢,殷宗泽. 土工原理与计算(第二版). 北京:中国水利水电出版社,1996
[131] 钱能. C++程序设计教程. 北京:清华大学出版社,1999
[132] 齐舒创作室. C++6.0 开发技巧及实例剖析. 北京:清华大学出版社,1999
[133] 康博创作室. Visual C++6.0 程序设计自学教程. 北京:清华大学出版社,2002
[134] 潘安平. 高层建筑和裙房连体筏板地基反力分布的探讨. 岩土工程技术,2003,(3)
[2] 宰金珉,宰金璋.高层建筑基础分析与设计——土与结构物共同作用的理论与应用.北京:中国建筑工业出版社,2001
[3] 张雄,刘岩.无网格法.北京:清华大学出版社,2004
[4] Belytschko T, Krongauz Y, Organ D. Meshless methods: An overview and recent development. Comput. Methods Appl. Mech. Engrg. ,1996,139:3-47
[5] 盂闻远,卓家寿.无网格的崛起与进展——一种新兴的数值方法评述.河海大学学报,1999,27(力学专辑):51-58
[6] 曹国金,姜弘道.无单元法研究和应用现状及动态.力学进展,2002,32(4):526-534
[7] 生跃,黄义.双参数弹性地基上自由矩形板.应用数学和力学,1987,8(4)
[8] 熊渊博.Kirchhoff 板问题的无网格局部 Petrov-Galerkin 方法研究[博士学位论文].长沙:湖南大学,2005
[9] 蔡长忠.弹性地基自由边圆形厚板在偏心集中力作用下弯曲问题的 Fourier 级数解.工程力学,1986,(4):27-39
[10] 石小平,姚祖康.Pasternak 基础上四边矩形厚板的解.同济大学学报,1989,17(2):173-184
[11] 宋启根,林洋,徐培.双参数地基 Reissner 板局部荷载解.岩土工程学报,1993,15(5):48-58
[12] 曲庆璋,梁兴复.不同支承条件矩形中厚板的精确解.上海力学,1997,18(1)
[13] J.T.Katsikadelis. The Analysis of Plates on Elastic Foundation by the Boundary Integral Equation Method. Thesis Presented to the Polytechnic Institute of New York, 1982
[14] J.T.Katsikadelis, A.E.Armenakas. Analysis of Clamped Plates on Elastic Foundation by the Boundary Integeral Equation Method. Journal of Applied Mechanics, 1984, Vol.51
[15] J.T.Katsikadelis and A.E.Armenakas,Plates on Elastic Foundation by BIE method. Journal of Engineering Mechanics, 1984,110(7)
[16] J.T.Katsikadelis and L.F.Kallivokas, Clamped Plates on Pasternaktype Elastic Foundation by the Boundary Element Method. Journal of Applied Mechanics, 1986, Vol.53
[17] J.Puttonen and P.Varpasuo, Boundary Element Analysis of a Plate on Elastic Foundations. Int .J.Numerical Methods in Engineering, 1986, Vol.23:287-303
[18] G.Bezine. A New Boundary Element Method for Bending of Plates on Elastic Foundations. Int.J.Solids Structures, 1988, 24(6):557-565
[19] E.J.Sapountzakis, J.T.Katsikadelis. Boundary Element Solution for Plates of VaribleThickness. Journal of Engineering Mechanics, 1991, 117(6)
[20] 邓安福,李正良.双参数地基上 Reissner 板弯曲问题的基本解.结构工程学报,1991,(3):244-249
[21] 邓安福,李正良.弹性地基上 Reissner 板的基本解.固体力学学报,1993,14(1)
[22] 李正良,邓安福.双参数地基上板弯曲问题的边界积分方程.应用数学和力学,1992,13(7):633-643
[23] 李正良,干腾君,邓安福.双参数弹性地基板的边界元法.重庆建筑工程学院学报,1995,17(1):1-7
[24] 江隆植等.纵横荷载共同作用下基础板弯曲问题样条边界元分析.上海力学,1990, (2):70-76
[25] 干腾君.空间框架—筏基—土共同工作的有限元—边界元耦合方法[硕士学位论文].重庆: 重庆建筑工程学院,1993
[26] Cheung Y. K., Zienkiewize O. C. Plates and tanks on elastic foundation – an application of finite element method. Int. J. Solids and Struc, 1965, (1):451-461
[27] Haddadin M. J. Mats and combined footings analysis by the finite element methods. J.ACI. 1971,68(2)
[28] Hain S. J., Lee I. K., Rational analysis of raft foundation. J. Geotech. Eng. Div., Proc. ASCE, 1974, 68(12)
[29] Sharma K. G., Nagpal A. K. , Grag M. K. Finite element analysis of rafts resting on elastic half space. Indian Geotechnical Journal, 1984,14(1):28-39
[30] 刘开国.地基—基础—框架体系相互作用的计算方法.建筑结构学报,1981,(5):55-72
[31] 宰金珉等.高层空间剪力墙结构与地基共同作用三维问题的双重扩大子结构有限元—有限层分析.建筑结构学报,1983,(5):57-70
[32] 朱百里,曹铭葆,魏道垛.框架结构与地基基础共同作用的数值分析——线性与非线性地基.同济大学学报,1982,(4):15-31
[33] 姚祖恩等.框架、筏基和土共同作用机理的探讨.岩土工程学报,1984,6:30-41
[34] 张季荣,蔡敏.弹性地基上片筏基础的有限单元法分析.浙江大学学报,1988,22:71-78
[35] 张祥等.双参数弹性地基上厚板的有限元边界元联合解法.岩土工程学报,1995,(1):46-52
[36] Krysl, P., Belytschko, T. Analysis of thin plates by the element-free Galerkin method. Comput. Mech., 1996,17:26-35
[37] Ouatouati,A.E., Johnson, D.A. A new approach for numerical modal analysis using the element free method. Int. J.Numer. Methods Eng., 1999, 46:1-27
[38] Liu,G.R., Chen, X. L. A mesh-free method for static and free vibration analyses of thin platesof complicated shape. J. Sound Vib., 2001, 241(5):839-855
[39] 张建辉,邓安福.无单元法在筏板基础计算中的应用.岩土工程学报, 1999,21(6):691-695
[40] 张建辉,邓安福.无单元法在弹性地基板计算中的应用.重庆建筑大学学报,1999,21(2):84-88
[41] 张伟星,庞辉.无单元法分析弹性地基板.力学与实践,2000,22(3):38-41
[42] 方电新,李卧东,王元汉.用无网格法计算平板弯曲问题.岩土力学,2001,22(3) :347-349
[43] Meyerhof,G. G. The Settlement Analysis of Building Frame. The Structural Engineer, 1947,25
[44] Meyerhof,G. G. Some Recent Foundation Research and its Application to Design, The Structure Engineer, 1953,31
[45] Chamecki. Structural Rigidty in Calculating Settlements. Jour.soil Mech.and Found. Div,ASCE,1956,82
[46] Przemienicki,J.S. Theory of Matrix Structural Analysis,1968
[47] Haddadin,M.M. Mats and Combined Footings Analysis by the Finite Element Methods. Proc, ACI, 1971, 68(12)
[48] Christian,J.T. Soil Structure-interaction for Tall Buildings. Planning and Design of Tall Buildings. Lehigh University, 1972,19
[49] King,G.J.W., Chandrasekaran. Interaction Analysis of a Rafted Multi-story Space Frame Resting on an Inhomogeneous Clay Stratum. Proc.Int.Conf.on Finite Elenent Methods in Engineering, Univ.of.N.S.w.Autralian, 1974
[50] Wardle,L.J., Fraser,R.A. Methods for Raft Foundation Design including Soil-Structure Interaction. Cooerative Project, The University of New South Wales,Australia, 1975
[51] Hooper,J.A., Wood,L.A. Foundation Analysis of a Cross-Wall Structure. Proc.Int.Conf.on Performance Big, Struc. Glasgow,1976
[52] Poulos,H.G., Davis,E.H. Pile Foundation Analysis and Design. John Wiley, New York, 1980
[53] Poulos,H.G., Soil-Structure Interaction—General Report(Preliminary). Proc.10th ICSMFE,1981
[54] 张问清,赵锡宏.逐步扩大子结构法计算高层结构刚度的基本原理.建筑结构学报,1980,(4):66-70
[55] 宰金珉,张问清,赵锡宏.平面形状为 L 形的空间剪力墙结构与不均匀的地基共同作用.岩土工程学报,1983,(2)
[56] 裴捷,张问清,赵锡宏.考虑填充墙的框架结构与地基基础共同作用的分析方法.建筑结构学报,1984,(4)
[57] 杨敏.上部结构与桩筏基础共同作用的理论与试验研究.[博士学位论文].上海:同济大学,1989
[58] 袁聚云,沈伟跃,赵锡宏.空间剪力墙结构—厚筏—桩—地基共同作用分析.上海高层建筑桩筏与桩箱基础设计理论.上海:同济大学出版社,1989
[59] 邓安福,干腾君,李正良.上部结构-筏式基础-地基共同作用分析的一种新方法.全国首届结构与介质相互作用学术会议论文集,1993
[60] 张保良,姜洪伟,赵锡宏.层状土中群桩沉降分析.上海力学,1996,(1)
[61] 中国建筑科学研究院主编.《建筑桩基技术规范》(JGJ094-94) .北京:中国建筑工业出版社,1995
[62] 叶于政,孙家乐.高层建筑箱形基础与地基和上部结构共同作用机理的初步探讨和采用弹性杆的简化计算方法.北京工业大学学报,1980,(3)
[63] 孙家乐,张雷.从高层建筑与地基基础相互作用研讨连续基础简化计算.第四届土力学基础工程学术会议论文集.北京:中国建筑工业出版社,1986
[64] 王兆清,冯伟.自然单元法研究进展.力学进展,2004,34(4):437-445
[65] 周瑞忠,周小平,吴琛.数值方法进展:从连续介质到离散粒子模型.工程力学,2005,22(增刊):228-239
[66] Gingold RA, Moraghan JJ. Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Mon. Not. Roy. Astrou. Soc., 1977, 18:375-389
[67] Liu W K, Jun S, Adee J, Belytschko T. Reproducing kernel particle methods. Int J Numer Methods Engrg, 1995, 38(10):1655-1679
[68] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. Int. J. for Num. Methods in Eng.,1994, 37:229-256
[69] Cordes LW, Moran B. Treatment of material discontinuity in the Element-free Galerkin method. Comput Meth Appl Mech Eng, 1996, 139: 3-47
[70] 庞作会,葛修润,郑宏等. 一种新的数值计算方法无网格伽辽金法. 计算力学学报,1999,18(5): 581-584
[71] Krongauz Y, Belytschko T. EFG approximation with discontinuous derivatives. Int J Num Meth Eng,1998,41:1215-1233
[72] Onate E, Idelsohn S, Zienkiewicz O C, Talor R L. A finite point method in computational mechanics application to convective transport and fluid flow. Int J Numer Methods Engrg, 1996, 39(22):3839-3866
[73] Duarte C A, Oden J T. Hp clouds: a h-p meshless method, Numerical Methods for Partical Differential Equations,1996,12:673-705
[74] Zhu T, Zhang J, Arluri S N. A meshless local boundary integral equation method for solving nonlinear problems. Computational Mechanics,1998,22(3):174-186
[75] Braun J, Sambridge M. A numerical method for solving partial differential equations on highly irregular evolving grids. Nature, 1995, 376: 655-660
[76] N. Sukumar and B. Moran and T. Belytschko. The natural element method in solid mechanics. 1998. International Journal for Numerical Methods in Engineering, 43(5):839-887.
[77] N. Sukumar and B. Moran and A. Yu. Semenov and V. V. Belikov. Natural neighbor Galerkin methods. International Journal for Numerical Methods in Engineering, 2001. 50(1):1-27.
[78] Sukumar N. Voronoi cell finite difference method for the diffusion operator on arbitary unstructured grids. Int J Num Meth Eng,2003,57:1-34
[79] Cueto E, Doblare M, Gracia L. Imposing essential boundary conditions in the natural element method by density-scaled α-shapes. Int J Num Meth Eng,2000,49:519-546
[80] 蔡永昌,李晓军,朱合华.基于局部 Petrov-Galerkin 过程的自然单元法及其面向对象的设计与实现. 岩石力学与工程学报,2003,22(8):1263-1268
[81] 蔡永昌,朱合华. 岩土工程数值计算中的无网格方法及其全自动布点技术. 岩土力学,2003,24(1):21-24
[82] 蔡永昌,朱合华,王建华. 基于 Voronoi 结构的无网格局部 Petrov-Galerkin 方法. 力学学报,2003,35(2):187-193
[83] 张雄,宋康祖,陆明万. 紧支试函数加权残量法. 强度与环境,2000,增刊: 58-63
[84] Zhang X, Song K Z, Lu M W, Chen Y. Imposition of essential boundary conditions by displacement constraint equations in meshless methods. Communications in Numrical Methods in Engineering, 2001, 17(3): 165-178
[85] Zhang X, Song K Z, Lu M W. Hermite type collocation with radial funcations. In: Proceedings of international conference on computational engineering & science, 2000, Los Angels. 1445-1450
[86] 刘欣,朱德懋,陆明万,张雄. 基于流形覆盖思想的无网格方法的研究. 计算力学学报,2001,18(1): 21-27
[87] 栾茂田,田荣,杨庆等. 有限覆盖无单元法在岩土类弱拉型材料接触摩擦问题中的应用.岩土工程学报,2002,24(2):137-141
[88] 张湘伟,蔡永昌. 一种改进的无单元法. 计算力学学报,2002.19(1): 26-30
[89] 秦荣. 样条无网格法. 见: 袁明武,孙树立编. 工程与科学中的计算力学,中国计算力学大会’2001 论文集,广州,2001 年 12 月 6-8 日. 北京: 北京大学出版社,2001. 327-332
[90] 何沛祥,李子然,吴长春. 无网格法与有限元的耦合及其对功能梯度材料断裂计算的应用. 中国科学技术大学学报,2001,31(6): 673-680
[91] 袁振,李子然,吴长春. 无网格法模拟复合型疲劳裂纹的扩展.工程力学,2002,19(1): 25-28
[92] 周忠瑞,周小平,缪冰. 小波基无单元法及其工程应用. 工程力学,2003,20(6): 70-74
[93] 屈智炯,土的塑性力学,成都,成都科技大学出版社, 第一版,1987
[94] 周进雄,李梅娥,张红艳,张陵. 再生核质点法研究进展,力学进展,2002,32(4)
[95] Liu W K, Jun S, Zhang Y F. Reproducing Kernel particle methods. Int J Numer Methods Engrg, 1995, 20:1081-1106
[96] Liu W K, Jun S, et al. Reproducing Kernel particle methods for structure dynamics. Int J Numer Methods Engrg, 1995, 38: 1655-1679
[97] Liu W K, Chen Y. Wavelet and multiple scale reproducing Kernel methods. Int J Numer Methods Fluids, 1995, 21: 901-931
[98] Liu W K, Chen Y, Uras R. A. Enrichment of the finite element method with reproducing Kernel particle method. In: Cory J J F, Gordon J L, eds. Current Topics in Computational Mechanics. ASME PVP, 1995, 305. 253-258
[99] 库东峰. 再生核粒子法及其在平板弯曲问题中的应用[硕士学位论文].南京:南京航空航天大学,2005
[100] 史宝军,袁明武,李君. 基于核重构思想的最小二乘配点型无网格方法. 力学学报,2003,35(6) : 697-706
[101] 史宝军,袁明武,孙树立,陈斌. 基于核重构思想的配点型无网格方法的研究——一维问题. 计算力学学报,2004,21(1) : 97-103
[102] Lu Y Y, Belytschko T, Gu L. A new implementation of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1994, 113: 397-414.
[103] 张建辉. 层状地基上桩筏基础的分析方法及其布桩优化研究[博士学位论文]. 重庆:重庆建筑大学,1999
[104] G. R. Liu. Mesh Free Methods: Moving Beyond the Finite Element Method. London:CRC Press,2002
[105] 蔡永昌,朱合华. 基于局部搜索算法的自然邻接点方法. 力学学报,2004,36(5) : 623-628.
[106] 朱怀球,吴江航. 一种基于 Voronoi Cells 的 C∞插值基函数及其在计算流体力学中的若干应用. 北京大学学报(自然科学版),2001,37(5):669-678.
[107] Green P J, Sibson R R. Computing dirichlet tessellations in the plane. The ComputerJournal,1978,21:168-173
[108] Hisamoto Hiyoshi. Study on interpolation based on Voronoi diagrams:[dissertation]. Tokyo:University of Tokyo,2000
[109] Belikov V and Semenov A. Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive generating isolines algorithm.Numerical Grid Generation in Computational Field Simulation, Proc. Of the 6th Intl. Conf. Greenwich Univ.July 1998
[110] Hisamoto Hiyoshi, Kokichi Sugihara. Two generalizations of an interpolant based Voronoi diagrams. International Journal of Shape Modeling, 1999,5(2):219-231
[111] 胡海昌. 弹性力学的变分原理及其应用. 北京:科学出版社,1987
[112] 张福范. 弹性薄板. 北京:科学出版社,1984
[113] 张建辉. 双参数地基板的无单元法. 岩土工程学报,2005,27(7):776-779
[114] 季求知,曲庆章.双参数弹性地基上四边自由矩形板问题. 青岛建筑工程学院学报,1996,17(3):85-93
[115] 王勖成,邵敏. 有限单元法基本原理和数值方法. 北京:清华大学出版社,1997.
[116] 包彦. 带裙房高层建筑与地基基础共同作用的理论应用与工程实践研究[博士学位论文].上海:同济大学,2003.12
[117] 曾祥勇,邓安福. 弹性地基上水工结构各向异性 Mindlin 底板计算分析的无单元法(EFGM).岩土力学,2006 增刊(2)
[118] 董建国,赵锡宏. 高层建筑地基基础——共同作用理论与实践. 上海:同济大学出版社,1997
[119] 黄义,何芳社. 弹性地基上的梁、板、壳. 北京:科学出版社,2005
[120] 孙卫明,杨光松,张承宗. 双参数地基上弹性厚板弯曲的一般解析解. 工程力学,1999,16(2):71-78
[121] 梁清香. 有限元与 marc 实现,机械工业出版社,第一版,2003
[122] 方世敏. 上部结构与地基基础共同工作的子结构分析法. 建筑结构学报,1980,(4)
[123] 陈希昌. 高层建筑物上部结构与基础及地基共同作用问题研究[博士学位论文]. 重庆:重庆建筑大学,1997
[124] 吴晓涵. 面向对象结构分析程序设计. 北京:科学出版社,2002,(4)
[125] 罗立平,赵锡宏. 空间框架结构——厚筏——地基共同作用分析. 上海高层建筑桩筏与桩箱基础设计理论. 上海:同济大学出版社,1989
[126] 干腾君. 考虑上部结构共同作用的筏板基础分析及其优化[博士学位论文]. 重庆:重庆大学,2001
[127] 陈卓. 上部结构、筏板、地基共同作用的面向对象有限元分析[硕士学位论文]. 重庆:重庆大学,2004,(5)
[128] A.P.S Selvadurai 著. 范文田等译. 土与基础相互作用的弹性分析. 北京:中国铁道出版社,1984
[129] 王元淳. 边界元法基础. 上海:上海交通大学出版社,1988
[130] 钱家欢,殷宗泽. 土工原理与计算(第二版). 北京:中国水利水电出版社,1996
[131] 钱能. C++程序设计教程. 北京:清华大学出版社,1999
[132] 齐舒创作室. C++6.0 开发技巧及实例剖析. 北京:清华大学出版社,1999
[133] 康博创作室. Visual C++6.0 程序设计自学教程. 北京:清华大学出版社,2002
[134] 潘安平. 高层建筑和裙房连体筏板地基反力分布的探讨. 岩土工程技术,2003,(3)