基于有限质点法的空间钢结构连续倒塌破坏研究
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摘要
本文以空间钢结构的连续倒塌破坏研究为主线,以向量式结构力学为理论基础,以有限质点法为手段,分别从几何破坏、材料破坏、构件断裂以及接触碰撞四个方面,通过理论推导和数值计算,对空间钢结构连续倒塌的全过程进行模拟,并对结构连续倒塌过程中的破坏机理进行研究。
基于向量式结构和固体力学理论,本文提出了一种结构分析的新方法——有限质点法。该方法以“点值描述”和“路径单元”为基本概念,以清晰的物理模型和质点运动控制方程描述结构行为,在结构的几何非线性、材料非线性以及不连续行为计算中有很大的优势。文中详细阐述了有限质点法的基本概念和原理,推导了该方法进行空间杆系结构和空间梁系结构的基本公式,以及结构中典型约束点及特殊运动点的内力计算公式,为空间钢结构连续倒塌研究奠定了理论基础,提供了分析方法。
建立了有限质点法进行结构几何非线性动力分析的基本框架,对空间钢结构的几何破坏问题进行了研究。首先验证了有限质点法在空间杆系和梁系结构几何非线性动、静力问题求解中的有效性,然后在此基础上对空间钢结构几何破坏中的两种典型破坏模式—失稳破坏和机构化破坏—进行模拟和分析。探讨了空间钢结构弹性失稳破坏的全过程跟踪方法,以及结构的失稳破坏机理。针对空间钢结构的机构化破坏问题,讨论了结构的体系分类。验证了有限质点法在动不定结构运动行为模拟中的有效性,并对空间钢结构的机构化破坏过程进行了分析。
发展了有限质点法进行结构弹塑性分析的基本流程,对空间钢结构的材料破坏进行了研究。建立了结构的弹塑性模型和单元屈服方程,通过对若干杆系和梁系结构的弹塑性分析,验证了有限质点法在结构弹塑性分析中的有效性。在考虑压杆失稳模型的基础上,分析结构的弹塑性失稳过程,研究了不同的本构模型对结构失稳模式的影响。为分析空间钢结构的动力弹塑性行为,建立了弹塑性模型加卸载过程中的应力判断准则和计算流程,对空间钢结构往复荷载下的滞回性能进行了模拟和分析。
提出了构件断裂的模拟算法,对空间钢结构构件的断裂行为进行了研究。基于材料试验和文献资料,建立了结构构件的断裂准则和断裂模式,给出了断裂发生后质点内力、外力、质量等的计算方法。从能量分析的角度出发,通过对若干数值算例的分析验证了断裂算法的合理性。结合结构的几何和材料非线性分析,对空间钢结构的断裂过程进行了分析。
提出了构件接触和碰撞模拟算法,对空间钢结构构件的接触和碰撞行为进行了研究。文中基于空间向量分析理论提出了结构空间运动中的接触侦测方法,然后根据碰撞类型的不同,分别建立了结构刚性体碰撞和柔性体碰撞模型,推导了有限质点法中结构碰撞反应的计算公式。通过对典型算例的分析,验证了结构接触侦测算法的准确性和结构碰撞反应算法的有效性。
综合以上各部分的分析和程序成果,以某空间悬挑网架在台风下的连续倒塌破坏为例,分别采用杆单元和梁单元对该结构在动荷载下的连续倒塌全过程进行逐步分析。通过将计算结果与现场破坏情形进行对比,验证了有限质点法在结构复杂行为分析中的有效性,也深入了解了该结构的连续倒塌破坏机理。
本文的研究工作模拟了空间钢结构的连续倒塌破坏的全过程,揭示了倒塌过程中的破坏机理,推进了空间钢结构连续倒塌研究的发展。同时,有限质点法的提出为工程师和研究者进行结构的复杂行为分析提供了新的方法和思路,具有一定的指导意义。
Based on the Finite Particle Method (FPM), this thesis carries out an intensive research regarding the simulation and analysis of progressive collapse for space steel structures. Not only nonlinear geometric and constitutive behaviors, but also fracture, contact and collide during the dynamic process of progressive collapse are taken into considerations in the research.
This thesis presents a structural analysis method called the Finite Particle Method (FPM) for structural progressive collapse simulation. Different from the traditional methods generated from continuum mechanics and variational principle, the FPM is based on the vector mechanics. With the description of "point value" and "path element", the FPM models the analyzed domain composed of finite particles whose motions are described by Newton's second law. Structural nonlinearities and discontinuities can be easily handled by this method, which is very advantageous in the simulation of structural failure. This work derives fundamentals of the FPM, including basic procedures, formulations of 3D bar element,3D beam element and internal force of particles containing special motion restrictions. The FPM is the basic method used in this work.
The framework of dynamic geometric nonlinear analysis of the FPM is developed, and analyses of geometric failure of space steel structures are presented. With several numerical examples, the accuracy and generability of the dynamic geometric nonlinear analysis program is demonstrated. Then, two kinds of typical geometric failures, buckling and mechanism failure, are simulated and analyzed. Different strategies for pre-and post-buckling simulation are given and discussed, which are successfully applied in the analysis of elastic buckling of space steel structures. The FPM is also verified in the motion analysis of kinematically indeterminate structures. Taking a double-layer grid structure as an example, the mechanism failure procedure of space steel structure is investigated.
The framework of elastic-plastic analysis based on the FPM is developed, and analyses of material failure of space steel structures are presented. The elastic-plastic model and yield equations of steel material are proposed. Several numerical examples are presented to prove the availability of the FPM in structural material failure analysis. And then the inelastic post-buckling behavior of space steel structures are compared and discussed with different constitutive models. Based on the stress incremental formulation and stress reversal model, hysteretic behavior of a double layer grid structure under cyclic loading is analyzed, which reveals the energy dissipation capability of space steel structures.
The algorithm considering structural member fracture during progressive collapse process is developed. Based on concepts of the FPM, the failure criterion and the failure modeling algorithm are proposed, respectively. According to the energy conservation study of a 2D truss, different kinds of energies are balanced during the fracture process, which verified the fracture algorithm in this work. Combining the nonlinearity analysis, fracture behaviors of several space steel structures are investigated.
The algorithms considering contact between structural members during the progressive collapse process are developed. The algorithm of contact determination is proposed based on the theory of 3D analytical geometry. According to different collide styles between members, the formulations of rigid and flexible collide are derived, respectively. Several numerical examples are presented to demonstrate the accuracy and capability of the contact algorithms.
The whole progressive collapse process of a cantilever steel structure is simulated and investigated using the programs developed in this work, providing more profound understanding of structural failure reasons.
This study advances the development of investigations of progressive collapse for space steel structures, and provides a basis for the further researches in this field. Meanwhile, it also promotes the applications of the Finite Particle Method into complicated structural behavior analysis.
基于向量式结构和固体力学理论,本文提出了一种结构分析的新方法——有限质点法。该方法以“点值描述”和“路径单元”为基本概念,以清晰的物理模型和质点运动控制方程描述结构行为,在结构的几何非线性、材料非线性以及不连续行为计算中有很大的优势。文中详细阐述了有限质点法的基本概念和原理,推导了该方法进行空间杆系结构和空间梁系结构的基本公式,以及结构中典型约束点及特殊运动点的内力计算公式,为空间钢结构连续倒塌研究奠定了理论基础,提供了分析方法。
建立了有限质点法进行结构几何非线性动力分析的基本框架,对空间钢结构的几何破坏问题进行了研究。首先验证了有限质点法在空间杆系和梁系结构几何非线性动、静力问题求解中的有效性,然后在此基础上对空间钢结构几何破坏中的两种典型破坏模式—失稳破坏和机构化破坏—进行模拟和分析。探讨了空间钢结构弹性失稳破坏的全过程跟踪方法,以及结构的失稳破坏机理。针对空间钢结构的机构化破坏问题,讨论了结构的体系分类。验证了有限质点法在动不定结构运动行为模拟中的有效性,并对空间钢结构的机构化破坏过程进行了分析。
发展了有限质点法进行结构弹塑性分析的基本流程,对空间钢结构的材料破坏进行了研究。建立了结构的弹塑性模型和单元屈服方程,通过对若干杆系和梁系结构的弹塑性分析,验证了有限质点法在结构弹塑性分析中的有效性。在考虑压杆失稳模型的基础上,分析结构的弹塑性失稳过程,研究了不同的本构模型对结构失稳模式的影响。为分析空间钢结构的动力弹塑性行为,建立了弹塑性模型加卸载过程中的应力判断准则和计算流程,对空间钢结构往复荷载下的滞回性能进行了模拟和分析。
提出了构件断裂的模拟算法,对空间钢结构构件的断裂行为进行了研究。基于材料试验和文献资料,建立了结构构件的断裂准则和断裂模式,给出了断裂发生后质点内力、外力、质量等的计算方法。从能量分析的角度出发,通过对若干数值算例的分析验证了断裂算法的合理性。结合结构的几何和材料非线性分析,对空间钢结构的断裂过程进行了分析。
提出了构件接触和碰撞模拟算法,对空间钢结构构件的接触和碰撞行为进行了研究。文中基于空间向量分析理论提出了结构空间运动中的接触侦测方法,然后根据碰撞类型的不同,分别建立了结构刚性体碰撞和柔性体碰撞模型,推导了有限质点法中结构碰撞反应的计算公式。通过对典型算例的分析,验证了结构接触侦测算法的准确性和结构碰撞反应算法的有效性。
综合以上各部分的分析和程序成果,以某空间悬挑网架在台风下的连续倒塌破坏为例,分别采用杆单元和梁单元对该结构在动荷载下的连续倒塌全过程进行逐步分析。通过将计算结果与现场破坏情形进行对比,验证了有限质点法在结构复杂行为分析中的有效性,也深入了解了该结构的连续倒塌破坏机理。
本文的研究工作模拟了空间钢结构的连续倒塌破坏的全过程,揭示了倒塌过程中的破坏机理,推进了空间钢结构连续倒塌研究的发展。同时,有限质点法的提出为工程师和研究者进行结构的复杂行为分析提供了新的方法和思路,具有一定的指导意义。
Based on the Finite Particle Method (FPM), this thesis carries out an intensive research regarding the simulation and analysis of progressive collapse for space steel structures. Not only nonlinear geometric and constitutive behaviors, but also fracture, contact and collide during the dynamic process of progressive collapse are taken into considerations in the research.
This thesis presents a structural analysis method called the Finite Particle Method (FPM) for structural progressive collapse simulation. Different from the traditional methods generated from continuum mechanics and variational principle, the FPM is based on the vector mechanics. With the description of "point value" and "path element", the FPM models the analyzed domain composed of finite particles whose motions are described by Newton's second law. Structural nonlinearities and discontinuities can be easily handled by this method, which is very advantageous in the simulation of structural failure. This work derives fundamentals of the FPM, including basic procedures, formulations of 3D bar element,3D beam element and internal force of particles containing special motion restrictions. The FPM is the basic method used in this work.
The framework of dynamic geometric nonlinear analysis of the FPM is developed, and analyses of geometric failure of space steel structures are presented. With several numerical examples, the accuracy and generability of the dynamic geometric nonlinear analysis program is demonstrated. Then, two kinds of typical geometric failures, buckling and mechanism failure, are simulated and analyzed. Different strategies for pre-and post-buckling simulation are given and discussed, which are successfully applied in the analysis of elastic buckling of space steel structures. The FPM is also verified in the motion analysis of kinematically indeterminate structures. Taking a double-layer grid structure as an example, the mechanism failure procedure of space steel structure is investigated.
The framework of elastic-plastic analysis based on the FPM is developed, and analyses of material failure of space steel structures are presented. The elastic-plastic model and yield equations of steel material are proposed. Several numerical examples are presented to prove the availability of the FPM in structural material failure analysis. And then the inelastic post-buckling behavior of space steel structures are compared and discussed with different constitutive models. Based on the stress incremental formulation and stress reversal model, hysteretic behavior of a double layer grid structure under cyclic loading is analyzed, which reveals the energy dissipation capability of space steel structures.
The algorithm considering structural member fracture during progressive collapse process is developed. Based on concepts of the FPM, the failure criterion and the failure modeling algorithm are proposed, respectively. According to the energy conservation study of a 2D truss, different kinds of energies are balanced during the fracture process, which verified the fracture algorithm in this work. Combining the nonlinearity analysis, fracture behaviors of several space steel structures are investigated.
The algorithms considering contact between structural members during the progressive collapse process are developed. The algorithm of contact determination is proposed based on the theory of 3D analytical geometry. According to different collide styles between members, the formulations of rigid and flexible collide are derived, respectively. Several numerical examples are presented to demonstrate the accuracy and capability of the contact algorithms.
The whole progressive collapse process of a cantilever steel structure is simulated and investigated using the programs developed in this work, providing more profound understanding of structural failure reasons.
This study advances the development of investigations of progressive collapse for space steel structures, and provides a basis for the further researches in this field. Meanwhile, it also promotes the applications of the Finite Particle Method into complicated structural behavior analysis.
引文
[1]American Society of Civil Engineers. ASCE 7-05 Minimum Design Loads for buildings and other Structures [S].2005.
[2]Geriengsak Kaewkulchai, Eric B. Williamson. Beam element formulation and solution procedure for dynamic progressive collapse analysis [J]. Computer and Structures,2004,82: 639-951.
[3]Cynthia Pearson, Norbert Delatte. Ronan point apartment tower collapse and its effect on buildong codes [J]. Journal of Performance of Constructed Facilities ASCE,2005,19(2): 172-177.
[4]J. E. Breen. Research workshop on progressive collapse of building structures:Summary report [R]. Department of Housing and Urban Development,1976.
[5]M. Van Laetham. Stability of a double-layer-grid space structure [C]. Proc 2nd Int Conf on Space Structure Guildford U.K.:Billing and Sons,1975,745-754.
[6]I. M. Collins. An investigation into the collapse behaviour of double-layer grids [C]. Proc 3rd Int Conf on Space Structure, London:Elsevier Applied Science,1984,400-405.
[7]El Sheikh. The effect composit action on the behavior of space structures [D] Cambridge U. K.:Cambridge University,1991.
[8]http://en.wikipedia.org/wiki/Oklahoma_City_bombing. [EB/OL].
[9]http://en.wikipedia.org/wiki/911_collapse. [EB/OL].
[10]D. Isobe, Y. Toi. Analysis of structurally discontinuous reinforced concrete building frames using the ASI technique [J]. Computer and Structures,2000,76(4):471-481.
[11]Zdenek P. Bazant, Mathieu Verdure. Mechanics of progressive collapse:learning from World Trade Center and building demolitions [J].2007.
[12]杜文风,张慧.空间结构[M].北京：中国电力出版社,2008.
[13]张文福.空间结构[M].北京：科学出版社,2005.
[14]董石麟.新型空间结构设计、分析与施工[M].北京：人民交通出版社,2006.
[15]D. B. Moore. Prevention of Progressive Collapse [C]. Workshop on Prevention of Progressive Collapse, Washington U. S.,1976.
[16]British Standard Institute. Structural Use of Concrete. Part 1:Code of Practice for Design and Construction [S].1997.
[17]National Research Council of Canada. National Building Code for Canada [S].1996.
[18]European Committee for Standardization. Eurocode 1 [S].2002.
[19]American Concrete Institute. ASI 318 [S].2002.
[20]U. S.:General Service Administration. Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects [S].2003.
[21]U. S.:General Service Administration. Unified Facilituies Criteria:Design of Structures to Resist Progressive Collapse [S].2003.
[22]Department of Defense. Design of Structures to Resist Progressive Collapse [S].2005.
[23]American Society of Civil Engineer. Minimum design loads for buildings and other structures [S]. Reston,2002.
[24]中华人民共和国建设部.混凝土结构设计规范[S].北京,2002.
[25]王晶,高磊,蒋玉明,石磊,李青狮.关于国外抗连续性倒塌设计规范的研究[J].爆破，2009,26(1)：27-41.
[26]梁益,陆新征,缭志伟,叶列平.结构的连续倒塌：规范介绍和比较[C].第六届全国工程安全防护学术会议,洛阳,2007.
[27]Federal Emergency Management Agency. NEHRP Guidelines for the Seismic Rehabilitation of Buildings [S].1997.
[28]Federal Emergency Management Agency. The Seismic Rehabilitation of Buildings [S]. 2000.
[29]Federal Emergency Management Agency. NEHRP Improvement of Nonlinear Static Seismic Analysis Procedures [S].2005.
[30]G. Kaewkulchai, E. B. Williamson. Dynamic behavior of planar frames during progressive collapse [C]. Proc 16th ASCE Engineering Mechanics Conference, Seattle U.S.,2003.
[31]J. Kim, T. Kim. Assessment of progressive collapse resisting capacity of steel moment frames [J]. Journal of Constructional steel Research,2009,65(1):169-179.
[32]Shalva Marjanishvili, Elizabeth Agnew. Comparison of Various Procedures for Progressive Collapse Analysis [J]. Journal of Performance of Constructed Facilities ASCE, 2006,20(4):365-374.
[33]M. H. Tsai, J. H. Lu, B. H. Lin. Progressive collapse analyses of a seismically designed building in Taiwan [C]. Proc 1st Int Workshop on Performance, Protection and Strengthening of Structure under Extreme Loading, Whistler, Canada,2007.
[34]陆新征,李易,叶列平,马一飞,梁益.钢筋混凝土框架结构抗连续倒塌设计方法的研究[J].工程力学，2008,25：150-157.
[35]Kyaw Myo Lynn, Daigoro Isobe. Structural collapse analysis of framed structures under impact loads using ASI-Gauss finite element method [J]. International Journal of Impact Engineering,2007,34:1500-1516.
[36]钱稼茹,纪晓东,范重,刘先明.国家体育场大跨度钢结构罕遇地震性能分析[J].建筑结构学报，2007,28(2)：17-25.
[37]D. Z. Yankelevsky, Y. S. Karinski. Dynamic elasto-plastic response of symmetrically loaded beams [J]. Computer and Structures,2000,76:445-459.
[38]J. Lellp, K. Torn. Shear and bending response of a rigid-plastic beam subjected to impulsive loading [J]. Journal of Impact Engineering,2005,31:1081-1095.
[39]D. Karagiozova, Marcilio Alves. Dynamic elastic-plastic buckling of structural elements:A review [J]. Applied mechnics reviews,2008,61(4):0408031-04080326.
[40]R. W. Clough. The finite element method in plane stress analysis [C]. Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, Paris,1960.
[41]Kyaw Myo Lynn, Daigoro Isobe. Finite element code for impact collapse problems [J]. International Journal for Numerical Methods in Engineering,2007,69:2538-2563.
[42]Z. Y. Zhang, G. H. Paulino, W. Celes. Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials [J]. International Journal for Numerical Methods in Engineering,2007,72:893-923.
[43]E. Onate, S. R. Idelsohn, F. Del Pin, R. Aubry. The particle finite element method:an overview [J]. International Journal for Computer Methods,2004,1(2):267-307.
[44]O. Kayser Herold, H. G. Matthies. Least squares finite element methods for fluid-structure interaction problems [J]. Computer and Structures,2005,83:191-207.
[45]P. A. Cundall, O. D. L. Strack. A Discrete Element Model for Granular Assemblies [J]. Geotechnique,1979,29(1):47-65.
[46]F. A. Tavarez. Discrete element method for modelling solid and particulate materials [D]: University of Wisconsin-Madison,2005.
[47]F. A. Tavarez, M. E. Plesha. Discrete element method for modelling solid and particulate materials [J]. International Journal for Numerical Methods in Engineering,2007,70:379-404.
[48]方韬,龚顺风,金伟良.混凝土结构破坏过程的离散单元法模拟[J].浙江大学学报(工学版),2004,38(7)：921-925.
[49]金伟良,方韬.钢筋混凝土框架结构破坏性能的离散单元法模拟[J].工程力学,2005,22(4)：67-73.
[50]Xinzheng Lu, Xuchuan Lin, Lieping Ye. Simulation of Structural Collapse with Coupled Finite Element-Discret Element Method [C]. Proc Computational Structural Engineering, Shanghai:Springer,2009,127-135.
[51]G H. Shi, R. E. Goodman. Discontinuous deformation analysis [C]. Proceedings of the 25th US Symposium on rock mechanics, Evanston, U.S.,1984.
[52]贾金河,于亚伦.应用有限元和DDA模拟框架结构建筑物拆除爆破[J].爆破，2001,18(1)：27-30.
[53]M. Y. Ma, P. Barbeau, D. Penumadu. Evaluation of active thrust on retaining walls using DDA [J]. Journal of Computing in Civil Engineering,1995,1:820-827.
[54]丁承先,王仲宇.向量式固体力学[R].2008.
[55]丁承先,王仲宇,吴东岳,王仁佐,庄清锵.运动解析与向量式有限元[R].中央大学工学院桥梁工程研究中心,2007.
[56]丁承先.拟真结构分析的力学基础[C].第四届海峡两岸结构与岩土工程学术研讨会论文集,杭州,2007,51-60.
[57]E. C. Ting, C. Shih, Y. K. Wang. Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element [J]. Journal of Mechanics,2004,20(2): 113-122.
[58]E. C. Ting, C. Shih, Y. K. Wang. Fundamentals of a vector form intrinsic finite element: Part II:plane solid element [J]. Journal of Mechanics,2004,20(2):123-132.
[59]C. Shih, Y. K. Wang, E. C. Ting. Fundamentals of a vector form intrinsic finite element: Part III:Convected material frame and examples [J]. Journal of Mechanics,2004,20(2): 133-143.
[60]T.Y. Wu,, R. Z. Wang, C. Y. Wang. Large deflection analysis of flexible planar frame [J]. Journal of the Chinese Institute of Engineers,2006,29(4):593-606.
[61]T. Y. Wu, E. C. Ting. Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element [J]. Thin-Walled Structures,2008,46:261-275.
[62]T. Y. Wu, J. J. Lee, E. C. Ting. Motion analysis of structures (MAS) for flexible multibody systems:planar motion of solids [J]. Multibody System Dynamics,2008,20:197-221.
[63]C. Y. Wang, R. Z. Wang, K. C. Tsai. Numerical simulation of the progressive failure and collapse of structure under seismic and impact loading [C]. The 4th International Conference on Earthquake Engineering, Taibei, Taiwan,2006.
[64]R. Z. Wang, C. L. Wu, K. C. Tsai, Y. S. Yang, B. Z. Lin. Structural collapse analysis of framed structures under seismic excitation [C]. The 14th World Conference on Earthquake Engineering, Beijing, China,2008.
[65]Ying Yu, Yaozhi Luo. Finite particle method for kinematically indeterminate bar assemblies [J]. Journal of Zhejiang University Science A,2009,10(5):667-676.
[66]Ying Yu, Yaozhi Luo. Motion analysis of deployable structures based on the rod hinge element by the finite particle method [J]. Proc ImechE Part G:Aerospace Engineering,2009, 223:156-171.
[67]Ying Yu, Glaucio H. Paulino, Yaozhi Luo. Finite particle method for progressive failure simulation of framed structures based on Finite Particle Method [J]. Journal of Structural Engineering ASCE,2010.
[68]O. C. Zienkiewicz, R. L. Taylor. Finite Element Method [M]. Butterworth-Heinemann, 2000.
[69]W. J. Lewis. Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs [J]. Computer and Structures,1984,18(6):989-997.
[70]H. Goldstein, C. Poole, J. Safko. Classical mechanics [M]. Massachusetts:Addision Wesley Publishing Co.,2002.
[71]S. Pellegrino. Deployable structure [M]. New York:SpringerWien,2001.
[72]Yaozhi Luo, Decan Mao. On a type of radially retractable plate structures [J]. International Journal of Solids and Structures,2006,44(10):3452-3467.
[73]C. Hoberman. Radial expansion retraction truss structure [P]. US,1991.
[74]J. J. Monaghan. Smoothed particle hydrodynamics [J]. Annu Rev Astron Astrophys,1992, 30:543-574.
[75]J. E. Goldberg, R. M. Richard. Analysis of nonlinear structures [J]. Journal of Structural Division ASCE,1963,89(4):333-351.
[76]D. S. Jagannathan, H. I. Epstein, P. Christiano. Fictitious strains due to rigid body rotation [J]. Journal of Structural Division ASCE,1975,101(11):2472-2476.
[77]P. Kohnke. Large deflection analysis of frame structures by fictitous forces [J]. International Journal for Numerical Methods in Engineering,1978,12:1279-1294.
[78]Y. B. Yang, H. T. Chiou. Rigid body motion test for nonlinear analysis with beam elements [J]. Journal of Structural Engineering ASCE,1987,113(9):1404-1419.
[79]L. J. Leu, Y. B. Yang. Effects of rigid body and stretching on nonlinear analysis of trusses [J]. Journal ofStructural Engineering ASCE,1990,116(10):2582-2598.
[80]Y. B. Yang, S. R. Kuo. Theory & Analysis of Nonlinear Framed Structures [M]. Prentice-Hall,1994.
[81]Y. B. Yang, L. J. Leu. Post-buckling analysis of steel space strucsses [J]. Journal of Structural Engineering ASCE,1991,117(12):3824-3828.
[82]P. M. A. Slaats, J. de Jongh, A. A. H. J. Sauren. Model reduction tools for nonlinear structural dynamics [J]. Computers and Structures,1995,54(6):1155-1171.
[83]王仁佐.向量式结构运动分析：国立中央大学,2005.
[84]Y. B. Yang, C. T. Yang, T. P. Chang, P. K. Chang. Effects of member buckling and yielding on ultimate strengths of space trusses [J]. Engineering Structures,1997,19(2):179-191.
[85]P. F. Pai. Large-deformation analysis of flexible beams [J]. international Journal of Solids and Structures,1996,33(9):1335-1353.
[86]C. C. Rankin, F. A. Brogan. An element independent co-rotational procedure for the treatment of large rotations [J]. Journal of Pressure Vessel Technology,1986,108:165-172.
[87]J. F. Doyle. Nonlinear analysis thin-walled structure statics, dynamics and stability [M]. New York:Springer,2001.
[88]K. Mattiasson. Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals [J]. International Journal for Numerical Methods in Engineering, 1981,17:145-153.
[89]S. L. Chan. Large deflection dynamics analysis of space frame [J]. Computer and Structures,1996,58(2):381-387.
[90]M. Papadrakakis. Post-buckling analysis of spatial structures by vector interation methods [J]. Computers and Structures,1981,14(5-6):393-402.
[91]J. L. Meek, H. S. Tan. Geometrically nonlinear analysis of space frames by an incremental iterative technique [J]. Computer Methods in Applied Mechanics and Engineeging,1984,47: 261-282.
[92]Minoru Shugyo. Elastoplastic large deflection analysis of three-dimensional steel frames [J]. Journal of Structure Engineering ASCE,2003,129(9):1259-1267.
[93]陈骥.钢结构稳定理论与设计[M].北京：科学出版社,2001.
[94]童根树.钢结构的平面内稳定[M].北京：中国建筑工业出版社,2005.
[95]G. Ramesh, C. S. Krishnamoorthy. Inelastic post-buckling analysis of truss structures by dynamic relaxation method [J]. International Journal for Numerical Methods in Engineering, 1994,37:3633-3657.
[96]Jinyu Lu, Yaozhi Luo. Pre-and post-buckling analysis of structures by geometrically nonlinear force method [C]. The 3rd International Conference on Steel and Composite Structures, Mancheste:Taylor & Francis,2007.
[97]喻莹,罗尧治.基于有限质点法的结构屈曲行为分析[J].工程力学，2009,23(10)：23-29.
[98]A. Kassimali, E. Bidhendi. Stability of trusses under dynamic loads [J]. Computer and Structures,1988,29(3):381-392.
[99]G. Shi, S. N. Alturi. Elasto-plastic large deformation analysis of space frames:a plastic-hinge and stress-based explicit derivation of tangent stiffness [J]. International Journal for Numerical Methods in Engineering,1988,26:589-615.
[100]M. S. Park, B. C. Lee. Geometrically non-linear and elsdtoplastic three-dimensional shear flexible beam element of Von-Mises-type hardening material [J]. International Journal for Numerical Methods in Engineering,1996,39:383-408.
[101]Goran Turkalj, Josip Brnic, Jasna Prpic-Orsic. ESA formulation for large displacement analysis of framed structures with elastic-plasticity [J]. Computer and Structures,2004,82: 2001-2013.
[102]P. Mata, S. Oller, A. H. Barbat. Static analysis of beam structures under nonlinear geometric and constitutive behavior [J]. Computer Methods in Applied Mechanics and Engineeging,2007,196:4458-4478.
[103]C. R. Calladine. Buckminster Fuller's "Tensegrity" structures and Clerk Maxwell's rules for the construction of stiff frames [J]. International Journal of Solids and Structures,1978,14: 161-172.
[104]S. Pellegrino, C. R. Calladine. Matrix analysis of statically and kinematically indeterminate frameworks [J]. International Journal of Solids and Structures,1986,22: 409-428.
[105]S. Pellegrino, C. R. Calladine. Matrix analysis of statically and kinematically indeterminate frameworks [J]. International Journal of Solids and Structures,1986,22(4): 409-828.
[106]H. Tanaka, Y. Hangai. Rigid body displacement and stabilization conditions of unstable truss structures [C]. Shells, Membranes and Space Frames Proceedings IASS Symposium, Osaka, Japan:Elsevier Science Publishers,1986,55-62.
[107]关富玲,赵孟良,侯国勇.考虑弹性变形的可展杆系结构展开分析[J].工程力学，2006,24(8)：100-104.
[108]罗尧治.索杆张力结构的数值分析理论研究[D]杭州：浙江大学,2000.
[109]陆金钰.动不定结构的平衡矩阵分析方法与理论研究[D]杭州：浙江大学,2008.
[110]Ying Yu, Yaozhi Luo, Li Li. Deployable membrane structure based on the Bennett linkage [J]. Proc ImechE Part G:Aerospace Engineering,2007,221(2):775-783.
[111]Yaozhi Luo, Ying Yu, Jingjing Liu. A retractable structure based on Bricard linkages and rotating rings of tetrahedral [J]. International Journal of Solids and Structures,2008, 45(620-630).
[112]F. V. Jensen. Concepts for retractableroof structures [D] Cambridge, London:University of Cambridge,2005.
[113]Ying Yu, Yaozhi Luo. Finite particle method for kinematically indeterminate bar assemblies [J]. Journal of Zhejiang University Science A,2009,10(5):669-676.
[114]Yaozhi Luo, Jinyu Lu. Geometrically nonlinear force method for assemblies with infinitesimal mechanisms [J]. Computer and Structures,2006,84(31):2194-2199.
[115]R. Levy, WR. Spillers. Analysis of geometrically nonlinear structures [M]. London: Champaign& Hall,1985.
[116]S. Pellegrino. Analysis of prestressed mechanisms [J]. International Journal of Solids and Structures,1990,26(12):1329-1350.
[117]J. Chilton, H. Isler. The engineer's contribution to temporary architecture [M]. London: Thomas Telford Publishing,2000.
[118]M. Balz, J. Bohm. Generating shell models and their realization by photogrammetric measurement [C]. Shell and Spatial Structures from Models to realization, IASS 2004 Symposium, Montpellier, France,2004.
[119]李娜.空间网格结构几何形态研究与实现[D]杭州：浙江大学,2009.
[120]A. Affan, C. R. Calladine. Initial bar tensions in pin-jointed assemblies [J]. International Journal of Space Structures,1989,4(1):1-16.
[121]A. Affan. Collapse of double-layer space grids [D] Cambridge U. K.:Cambridge University,1987.
[122]D. Z. Yankelevsky. Elastic-plastic behavior of a shallow two bar truss [J]. International Journal of Mechanical Sciences,1999,41:663-675.
[123]P. G. Jr. Hodge, K. J. Bathe. Causes and consequences of nonuniqueness in an elastic/perfectly-plastic truss [J]. Journal of Applied Mechanics ASME,1986,53:235-241.
[124]S. R. Reid, T. X. Yu, J. L. Yang. Dynamic elastic-plastic behavior of whipping pipes Experiments and theoretical model [J]. International Journal of Inpact Engineering, 1996,18:703-733.
[125]H. Zhang, X. Zhang, J. S. Chen. A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems [J]. Computer and Structures,2003,81: 1739-1749.
[126]Huu-Tai Thai, Seung-Eock Kim. Large deflection inelastic analysis of space trusses using generalized displacement control method [J].Journal of Constructional steel Research, 2009,65:1987-1994.
[127]S.E. Kim, M.H. Park, S. H. Choi. Practical advanced analysis and design of three-dimensional truss bridge [J]. Journal of Constructional steel Research,2001,57: 907-923.
[128]Larissa Driemeier, Sergio P. Baroncini Proenc, Marcilio Alves. A contribution to the numerical nonlinear analysis of three-dimensional truss systems considering large strains, damage and plasticity [J]. Communications in Nonlinear Science and Numerical Simulation, 2005,10:515-535.
[129]T. Y. Yang, S. Saigal. A simple element for static and dynamic response of beams with material and geometric nonlinearities [J]. International Journal for Numerical Methods in Engineering,1984,20:851-867.
[130]N. Gebbeken. A refined numerical approach for the ultimate-load analysis of 3-D steel rod structures [J]. Engineering Computers,1998,15(3):312-344.
[131]W. S. King. A modified stiffness method for plastic analysis of semirigid frames [J]. Journal of Structural Division ASCE,1994,16(3):2156-2175.
[132]Afsin Saritas. Modeling of inelastic behavior of curved members with a mixed formulation beam element [J]. Finite Elements in Analysis and Design,2009,45:357-368.
[133]孙炳楠,洪涛,杨骊先.工程弹塑性力学[M].杭州：浙江大学出版社,2005.
[134]徐秉业,刘信声.应用弹塑性力学[M].北京：清华大学出版社,1995.
[135]W. J. Strong, T. X. Yu. Dynamic models for structural plasticity [M]. London: Springer-Verlag,1993.
[136]AASHTO. AASHTO LRFD Bridge Design Specification [S].1998.
[137]S. C. Tang, K. S. Yeung, C. T. Chon. On the tangent stiffness matrix in convected coordinate system [J]. Computers and Structures,1980,12:849-856.
[138]G. E. Blandford. Review of progressive failure analyses for truss structures [J]. Journal of Structure Engineering ASCE,1997,123(2):122-129.
[139]M. Papadrakakis. Inelastic post buckling analysis of trusses [J]. Journal of Structure Engineering ASCE,1983,109(9):2129-2147.
[140]C. D. Hill, G E. Blandford. Post-buckling analysis of steel space trusses [J]. Journal of Structure Engineering ASCE,1989,115(4):900-919.
[141]G. E. Blandford. Large deformation analysis of inelastic space truss structures [J]. Journal of Structure Engineering ASCE,1996,122(4):405-415.
[142]L. Kahn, R. Hanson. Inelastic cycle of axially loaded steel members [J]. Journal of Structure Engineering ASCE,1976,102(5):947-959.
[143]X. Q. Wu, C. Liu, T. X. Yu. A bifurcation phenomenon in an elastic-plastic symmetrical shallow truss subjected to a symmetrical load [J]. International Journal of Solids and Structures,1987,23(9):1225-1233.
[144]顾强.钢结构滞回性能及抗震设计[M].北京：中国建筑工业出版社,2009.
[145]朱世哲.双拱型空间钢管结构闸门的分析理论和试验研究杭州：浙江大学,2007.
[146]蔺海荣,冯维明,虞松.材料力学[M].北京：国防工业出版社,2001.
[147]Steen Krenk. Energy conservation in Newmark based time integration algorithms [J]. Computer Methods in Applied Mechanics and Engineeging,2006,195:6110-6124.
[148]J. M. Solberg, P. Papadopoulos. A finite element method for contact/impact [J]. Finite Elements in Analysis and Design,1998,1998(30):297-311.
[149]K. J. Bathe, P. A. Bouzinov. On the constraint function method for contact problems [J]. Computers and Structures,1997,64(5-6):1069-1085.
[150]凌道盛,徐兴.非线性有限元及程序[M].杭州：浙江大学出版社,2004.
[151]T. J. R. Hughes, R. L. Taylor, J. L. Sackman. A finite element method for a class of contact-impact problems [J]. Computer Methods in Applied Mechanics and Engineeging,1976, 8:249-276.
[152]A. B. Chaudhary, K. J. Bathe. A solution method for static and dynamic analysis of three-dimentional contact problems with friction [J]. Computers and Structures,1986,24: 855-873.
[153]J. T. Oden, N. Kikuchi. Finite element methods for constrained problems in elasticity [J]. International Journal for Numerical Methods in Engineering,1982,18:701-725.
[154]P. Papadopoulos, R. L. Taylor. A mixed formulation for the finite element solution of contact problems [J]. Computer Methods in Applied Mechanics and Engineeging,1992,94: 373-389.
[155]C. K. Choi, G. T. Chung. A gap element for three-dimensinal elasto-plastic contact problems [J]. Computers and Structures,1996,61(6):1155-1167.
[156]H. Schafer. A contribution to the solution of contact problems with the aid of bond elements [J]. Computer Methods in Applied Mechanics and Engineeging,1975,6:335-354.
[157]B. F. Maison, K. Kasai. Dynamics of pounding when two buildings collide [J]. Structures of Engineering ASCE,1992,21:771-786.
[158]吕林根,许子道.解析几何[M].北京：高等教育出版社,1987.
[159]J. A. Zukas, T. Nicholas, H. F. Swift, L. B. Greszczuk, D. R. Curran. Inpact dynamics [M]. New York:Wiley,1982.
[160]W. J. Stronge. Impact mechanics [M]. Cambridge, U. K.:Cambridge University Press, 2000.
[161]张雷明,刘西拉.钢筋混凝土结构倒塌分析的前沿研究[J].地震工程与工程振动,2003,23(3)：47-52.
[162]G. Kaewkulchai, E.B. Williamson. Modeling the Impact of failed members for progressive collapse analysis of frame structures [J]. Journal of Performance of Constructed Facilities ASCE,2006,20(4):375-383.
[163]赵凯华,罗蔚茵.新概念物理教程：力学[M].北京：高等教育出版社,2004.
[164]W. Goldsmith. Impact:The theory and physical behaviour of colliding solids [M]. London:Edword Arnold,1960.
[165]P. Wriggers, T. Vu Van, E. Stein. Finite element formulation of large deformation impact-contact problems with friction [J]. Computers and Structures,1990,37(3):319-331.
[166]欧进萍,段忠东,常亮.中国东南沿海重点城市台风危险性分析[J].自然灾害学报，2002,11(4)：9-17.
[167]曲晓宁,罗尧治,郑君华.悬挑网架在台风作用下的破坏机理研究[J].科技通报,2009,25(1)：77-82.
[168]中华人民共和国建设部.建筑结构荷载规范[S].北京,2002.
[2]Geriengsak Kaewkulchai, Eric B. Williamson. Beam element formulation and solution procedure for dynamic progressive collapse analysis [J]. Computer and Structures,2004,82: 639-951.
[3]Cynthia Pearson, Norbert Delatte. Ronan point apartment tower collapse and its effect on buildong codes [J]. Journal of Performance of Constructed Facilities ASCE,2005,19(2): 172-177.
[4]J. E. Breen. Research workshop on progressive collapse of building structures:Summary report [R]. Department of Housing and Urban Development,1976.
[5]M. Van Laetham. Stability of a double-layer-grid space structure [C]. Proc 2nd Int Conf on Space Structure Guildford U.K.:Billing and Sons,1975,745-754.
[6]I. M. Collins. An investigation into the collapse behaviour of double-layer grids [C]. Proc 3rd Int Conf on Space Structure, London:Elsevier Applied Science,1984,400-405.
[7]El Sheikh. The effect composit action on the behavior of space structures [D] Cambridge U. K.:Cambridge University,1991.
[8]http://en.wikipedia.org/wiki/Oklahoma_City_bombing. [EB/OL].
[9]http://en.wikipedia.org/wiki/911_collapse. [EB/OL].
[10]D. Isobe, Y. Toi. Analysis of structurally discontinuous reinforced concrete building frames using the ASI technique [J]. Computer and Structures,2000,76(4):471-481.
[11]Zdenek P. Bazant, Mathieu Verdure. Mechanics of progressive collapse:learning from World Trade Center and building demolitions [J].2007.
[12]杜文风,张慧.空间结构[M].北京：中国电力出版社,2008.
[13]张文福.空间结构[M].北京：科学出版社,2005.
[14]董石麟.新型空间结构设计、分析与施工[M].北京：人民交通出版社,2006.
[15]D. B. Moore. Prevention of Progressive Collapse [C]. Workshop on Prevention of Progressive Collapse, Washington U. S.,1976.
[16]British Standard Institute. Structural Use of Concrete. Part 1:Code of Practice for Design and Construction [S].1997.
[17]National Research Council of Canada. National Building Code for Canada [S].1996.
[18]European Committee for Standardization. Eurocode 1 [S].2002.
[19]American Concrete Institute. ASI 318 [S].2002.
[20]U. S.:General Service Administration. Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects [S].2003.
[21]U. S.:General Service Administration. Unified Facilituies Criteria:Design of Structures to Resist Progressive Collapse [S].2003.
[22]Department of Defense. Design of Structures to Resist Progressive Collapse [S].2005.
[23]American Society of Civil Engineer. Minimum design loads for buildings and other structures [S]. Reston,2002.
[24]中华人民共和国建设部.混凝土结构设计规范[S].北京,2002.
[25]王晶,高磊,蒋玉明,石磊,李青狮.关于国外抗连续性倒塌设计规范的研究[J].爆破，2009,26(1)：27-41.
[26]梁益,陆新征,缭志伟,叶列平.结构的连续倒塌：规范介绍和比较[C].第六届全国工程安全防护学术会议,洛阳,2007.
[27]Federal Emergency Management Agency. NEHRP Guidelines for the Seismic Rehabilitation of Buildings [S].1997.
[28]Federal Emergency Management Agency. The Seismic Rehabilitation of Buildings [S]. 2000.
[29]Federal Emergency Management Agency. NEHRP Improvement of Nonlinear Static Seismic Analysis Procedures [S].2005.
[30]G. Kaewkulchai, E. B. Williamson. Dynamic behavior of planar frames during progressive collapse [C]. Proc 16th ASCE Engineering Mechanics Conference, Seattle U.S.,2003.
[31]J. Kim, T. Kim. Assessment of progressive collapse resisting capacity of steel moment frames [J]. Journal of Constructional steel Research,2009,65(1):169-179.
[32]Shalva Marjanishvili, Elizabeth Agnew. Comparison of Various Procedures for Progressive Collapse Analysis [J]. Journal of Performance of Constructed Facilities ASCE, 2006,20(4):365-374.
[33]M. H. Tsai, J. H. Lu, B. H. Lin. Progressive collapse analyses of a seismically designed building in Taiwan [C]. Proc 1st Int Workshop on Performance, Protection and Strengthening of Structure under Extreme Loading, Whistler, Canada,2007.
[34]陆新征,李易,叶列平,马一飞,梁益.钢筋混凝土框架结构抗连续倒塌设计方法的研究[J].工程力学，2008,25：150-157.
[35]Kyaw Myo Lynn, Daigoro Isobe. Structural collapse analysis of framed structures under impact loads using ASI-Gauss finite element method [J]. International Journal of Impact Engineering,2007,34:1500-1516.
[36]钱稼茹,纪晓东,范重,刘先明.国家体育场大跨度钢结构罕遇地震性能分析[J].建筑结构学报，2007,28(2)：17-25.
[37]D. Z. Yankelevsky, Y. S. Karinski. Dynamic elasto-plastic response of symmetrically loaded beams [J]. Computer and Structures,2000,76:445-459.
[38]J. Lellp, K. Torn. Shear and bending response of a rigid-plastic beam subjected to impulsive loading [J]. Journal of Impact Engineering,2005,31:1081-1095.
[39]D. Karagiozova, Marcilio Alves. Dynamic elastic-plastic buckling of structural elements:A review [J]. Applied mechnics reviews,2008,61(4):0408031-04080326.
[40]R. W. Clough. The finite element method in plane stress analysis [C]. Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, Paris,1960.
[41]Kyaw Myo Lynn, Daigoro Isobe. Finite element code for impact collapse problems [J]. International Journal for Numerical Methods in Engineering,2007,69:2538-2563.
[42]Z. Y. Zhang, G. H. Paulino, W. Celes. Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials [J]. International Journal for Numerical Methods in Engineering,2007,72:893-923.
[43]E. Onate, S. R. Idelsohn, F. Del Pin, R. Aubry. The particle finite element method:an overview [J]. International Journal for Computer Methods,2004,1(2):267-307.
[44]O. Kayser Herold, H. G. Matthies. Least squares finite element methods for fluid-structure interaction problems [J]. Computer and Structures,2005,83:191-207.
[45]P. A. Cundall, O. D. L. Strack. A Discrete Element Model for Granular Assemblies [J]. Geotechnique,1979,29(1):47-65.
[46]F. A. Tavarez. Discrete element method for modelling solid and particulate materials [D]: University of Wisconsin-Madison,2005.
[47]F. A. Tavarez, M. E. Plesha. Discrete element method for modelling solid and particulate materials [J]. International Journal for Numerical Methods in Engineering,2007,70:379-404.
[48]方韬,龚顺风,金伟良.混凝土结构破坏过程的离散单元法模拟[J].浙江大学学报(工学版),2004,38(7)：921-925.
[49]金伟良,方韬.钢筋混凝土框架结构破坏性能的离散单元法模拟[J].工程力学,2005,22(4)：67-73.
[50]Xinzheng Lu, Xuchuan Lin, Lieping Ye. Simulation of Structural Collapse with Coupled Finite Element-Discret Element Method [C]. Proc Computational Structural Engineering, Shanghai:Springer,2009,127-135.
[51]G H. Shi, R. E. Goodman. Discontinuous deformation analysis [C]. Proceedings of the 25th US Symposium on rock mechanics, Evanston, U.S.,1984.
[52]贾金河,于亚伦.应用有限元和DDA模拟框架结构建筑物拆除爆破[J].爆破，2001,18(1)：27-30.
[53]M. Y. Ma, P. Barbeau, D. Penumadu. Evaluation of active thrust on retaining walls using DDA [J]. Journal of Computing in Civil Engineering,1995,1:820-827.
[54]丁承先,王仲宇.向量式固体力学[R].2008.
[55]丁承先,王仲宇,吴东岳,王仁佐,庄清锵.运动解析与向量式有限元[R].中央大学工学院桥梁工程研究中心,2007.
[56]丁承先.拟真结构分析的力学基础[C].第四届海峡两岸结构与岩土工程学术研讨会论文集,杭州,2007,51-60.
[57]E. C. Ting, C. Shih, Y. K. Wang. Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element [J]. Journal of Mechanics,2004,20(2): 113-122.
[58]E. C. Ting, C. Shih, Y. K. Wang. Fundamentals of a vector form intrinsic finite element: Part II:plane solid element [J]. Journal of Mechanics,2004,20(2):123-132.
[59]C. Shih, Y. K. Wang, E. C. Ting. Fundamentals of a vector form intrinsic finite element: Part III:Convected material frame and examples [J]. Journal of Mechanics,2004,20(2): 133-143.
[60]T.Y. Wu,, R. Z. Wang, C. Y. Wang. Large deflection analysis of flexible planar frame [J]. Journal of the Chinese Institute of Engineers,2006,29(4):593-606.
[61]T. Y. Wu, E. C. Ting. Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element [J]. Thin-Walled Structures,2008,46:261-275.
[62]T. Y. Wu, J. J. Lee, E. C. Ting. Motion analysis of structures (MAS) for flexible multibody systems:planar motion of solids [J]. Multibody System Dynamics,2008,20:197-221.
[63]C. Y. Wang, R. Z. Wang, K. C. Tsai. Numerical simulation of the progressive failure and collapse of structure under seismic and impact loading [C]. The 4th International Conference on Earthquake Engineering, Taibei, Taiwan,2006.
[64]R. Z. Wang, C. L. Wu, K. C. Tsai, Y. S. Yang, B. Z. Lin. Structural collapse analysis of framed structures under seismic excitation [C]. The 14th World Conference on Earthquake Engineering, Beijing, China,2008.
[65]Ying Yu, Yaozhi Luo. Finite particle method for kinematically indeterminate bar assemblies [J]. Journal of Zhejiang University Science A,2009,10(5):667-676.
[66]Ying Yu, Yaozhi Luo. Motion analysis of deployable structures based on the rod hinge element by the finite particle method [J]. Proc ImechE Part G:Aerospace Engineering,2009, 223:156-171.
[67]Ying Yu, Glaucio H. Paulino, Yaozhi Luo. Finite particle method for progressive failure simulation of framed structures based on Finite Particle Method [J]. Journal of Structural Engineering ASCE,2010.
[68]O. C. Zienkiewicz, R. L. Taylor. Finite Element Method [M]. Butterworth-Heinemann, 2000.
[69]W. J. Lewis. Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs [J]. Computer and Structures,1984,18(6):989-997.
[70]H. Goldstein, C. Poole, J. Safko. Classical mechanics [M]. Massachusetts:Addision Wesley Publishing Co.,2002.
[71]S. Pellegrino. Deployable structure [M]. New York:SpringerWien,2001.
[72]Yaozhi Luo, Decan Mao. On a type of radially retractable plate structures [J]. International Journal of Solids and Structures,2006,44(10):3452-3467.
[73]C. Hoberman. Radial expansion retraction truss structure [P]. US,1991.
[74]J. J. Monaghan. Smoothed particle hydrodynamics [J]. Annu Rev Astron Astrophys,1992, 30:543-574.
[75]J. E. Goldberg, R. M. Richard. Analysis of nonlinear structures [J]. Journal of Structural Division ASCE,1963,89(4):333-351.
[76]D. S. Jagannathan, H. I. Epstein, P. Christiano. Fictitious strains due to rigid body rotation [J]. Journal of Structural Division ASCE,1975,101(11):2472-2476.
[77]P. Kohnke. Large deflection analysis of frame structures by fictitous forces [J]. International Journal for Numerical Methods in Engineering,1978,12:1279-1294.
[78]Y. B. Yang, H. T. Chiou. Rigid body motion test for nonlinear analysis with beam elements [J]. Journal of Structural Engineering ASCE,1987,113(9):1404-1419.
[79]L. J. Leu, Y. B. Yang. Effects of rigid body and stretching on nonlinear analysis of trusses [J]. Journal ofStructural Engineering ASCE,1990,116(10):2582-2598.
[80]Y. B. Yang, S. R. Kuo. Theory & Analysis of Nonlinear Framed Structures [M]. Prentice-Hall,1994.
[81]Y. B. Yang, L. J. Leu. Post-buckling analysis of steel space strucsses [J]. Journal of Structural Engineering ASCE,1991,117(12):3824-3828.
[82]P. M. A. Slaats, J. de Jongh, A. A. H. J. Sauren. Model reduction tools for nonlinear structural dynamics [J]. Computers and Structures,1995,54(6):1155-1171.
[83]王仁佐.向量式结构运动分析：国立中央大学,2005.
[84]Y. B. Yang, C. T. Yang, T. P. Chang, P. K. Chang. Effects of member buckling and yielding on ultimate strengths of space trusses [J]. Engineering Structures,1997,19(2):179-191.
[85]P. F. Pai. Large-deformation analysis of flexible beams [J]. international Journal of Solids and Structures,1996,33(9):1335-1353.
[86]C. C. Rankin, F. A. Brogan. An element independent co-rotational procedure for the treatment of large rotations [J]. Journal of Pressure Vessel Technology,1986,108:165-172.
[87]J. F. Doyle. Nonlinear analysis thin-walled structure statics, dynamics and stability [M]. New York:Springer,2001.
[88]K. Mattiasson. Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals [J]. International Journal for Numerical Methods in Engineering, 1981,17:145-153.
[89]S. L. Chan. Large deflection dynamics analysis of space frame [J]. Computer and Structures,1996,58(2):381-387.
[90]M. Papadrakakis. Post-buckling analysis of spatial structures by vector interation methods [J]. Computers and Structures,1981,14(5-6):393-402.
[91]J. L. Meek, H. S. Tan. Geometrically nonlinear analysis of space frames by an incremental iterative technique [J]. Computer Methods in Applied Mechanics and Engineeging,1984,47: 261-282.
[92]Minoru Shugyo. Elastoplastic large deflection analysis of three-dimensional steel frames [J]. Journal of Structure Engineering ASCE,2003,129(9):1259-1267.
[93]陈骥.钢结构稳定理论与设计[M].北京：科学出版社,2001.
[94]童根树.钢结构的平面内稳定[M].北京：中国建筑工业出版社,2005.
[95]G. Ramesh, C. S. Krishnamoorthy. Inelastic post-buckling analysis of truss structures by dynamic relaxation method [J]. International Journal for Numerical Methods in Engineering, 1994,37:3633-3657.
[96]Jinyu Lu, Yaozhi Luo. Pre-and post-buckling analysis of structures by geometrically nonlinear force method [C]. The 3rd International Conference on Steel and Composite Structures, Mancheste:Taylor & Francis,2007.
[97]喻莹,罗尧治.基于有限质点法的结构屈曲行为分析[J].工程力学，2009,23(10)：23-29.
[98]A. Kassimali, E. Bidhendi. Stability of trusses under dynamic loads [J]. Computer and Structures,1988,29(3):381-392.
[99]G. Shi, S. N. Alturi. Elasto-plastic large deformation analysis of space frames:a plastic-hinge and stress-based explicit derivation of tangent stiffness [J]. International Journal for Numerical Methods in Engineering,1988,26:589-615.
[100]M. S. Park, B. C. Lee. Geometrically non-linear and elsdtoplastic three-dimensional shear flexible beam element of Von-Mises-type hardening material [J]. International Journal for Numerical Methods in Engineering,1996,39:383-408.
[101]Goran Turkalj, Josip Brnic, Jasna Prpic-Orsic. ESA formulation for large displacement analysis of framed structures with elastic-plasticity [J]. Computer and Structures,2004,82: 2001-2013.
[102]P. Mata, S. Oller, A. H. Barbat. Static analysis of beam structures under nonlinear geometric and constitutive behavior [J]. Computer Methods in Applied Mechanics and Engineeging,2007,196:4458-4478.
[103]C. R. Calladine. Buckminster Fuller's "Tensegrity" structures and Clerk Maxwell's rules for the construction of stiff frames [J]. International Journal of Solids and Structures,1978,14: 161-172.
[104]S. Pellegrino, C. R. Calladine. Matrix analysis of statically and kinematically indeterminate frameworks [J]. International Journal of Solids and Structures,1986,22: 409-428.
[105]S. Pellegrino, C. R. Calladine. Matrix analysis of statically and kinematically indeterminate frameworks [J]. International Journal of Solids and Structures,1986,22(4): 409-828.
[106]H. Tanaka, Y. Hangai. Rigid body displacement and stabilization conditions of unstable truss structures [C]. Shells, Membranes and Space Frames Proceedings IASS Symposium, Osaka, Japan:Elsevier Science Publishers,1986,55-62.
[107]关富玲,赵孟良,侯国勇.考虑弹性变形的可展杆系结构展开分析[J].工程力学，2006,24(8)：100-104.
[108]罗尧治.索杆张力结构的数值分析理论研究[D]杭州：浙江大学,2000.
[109]陆金钰.动不定结构的平衡矩阵分析方法与理论研究[D]杭州：浙江大学,2008.
[110]Ying Yu, Yaozhi Luo, Li Li. Deployable membrane structure based on the Bennett linkage [J]. Proc ImechE Part G:Aerospace Engineering,2007,221(2):775-783.
[111]Yaozhi Luo, Ying Yu, Jingjing Liu. A retractable structure based on Bricard linkages and rotating rings of tetrahedral [J]. International Journal of Solids and Structures,2008, 45(620-630).
[112]F. V. Jensen. Concepts for retractableroof structures [D] Cambridge, London:University of Cambridge,2005.
[113]Ying Yu, Yaozhi Luo. Finite particle method for kinematically indeterminate bar assemblies [J]. Journal of Zhejiang University Science A,2009,10(5):669-676.
[114]Yaozhi Luo, Jinyu Lu. Geometrically nonlinear force method for assemblies with infinitesimal mechanisms [J]. Computer and Structures,2006,84(31):2194-2199.
[115]R. Levy, WR. Spillers. Analysis of geometrically nonlinear structures [M]. London: Champaign& Hall,1985.
[116]S. Pellegrino. Analysis of prestressed mechanisms [J]. International Journal of Solids and Structures,1990,26(12):1329-1350.
[117]J. Chilton, H. Isler. The engineer's contribution to temporary architecture [M]. London: Thomas Telford Publishing,2000.
[118]M. Balz, J. Bohm. Generating shell models and their realization by photogrammetric measurement [C]. Shell and Spatial Structures from Models to realization, IASS 2004 Symposium, Montpellier, France,2004.
[119]李娜.空间网格结构几何形态研究与实现[D]杭州：浙江大学,2009.
[120]A. Affan, C. R. Calladine. Initial bar tensions in pin-jointed assemblies [J]. International Journal of Space Structures,1989,4(1):1-16.
[121]A. Affan. Collapse of double-layer space grids [D] Cambridge U. K.:Cambridge University,1987.
[122]D. Z. Yankelevsky. Elastic-plastic behavior of a shallow two bar truss [J]. International Journal of Mechanical Sciences,1999,41:663-675.
[123]P. G. Jr. Hodge, K. J. Bathe. Causes and consequences of nonuniqueness in an elastic/perfectly-plastic truss [J]. Journal of Applied Mechanics ASME,1986,53:235-241.
[124]S. R. Reid, T. X. Yu, J. L. Yang. Dynamic elastic-plastic behavior of whipping pipes Experiments and theoretical model [J]. International Journal of Inpact Engineering, 1996,18:703-733.
[125]H. Zhang, X. Zhang, J. S. Chen. A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems [J]. Computer and Structures,2003,81: 1739-1749.
[126]Huu-Tai Thai, Seung-Eock Kim. Large deflection inelastic analysis of space trusses using generalized displacement control method [J].Journal of Constructional steel Research, 2009,65:1987-1994.
[127]S.E. Kim, M.H. Park, S. H. Choi. Practical advanced analysis and design of three-dimensional truss bridge [J]. Journal of Constructional steel Research,2001,57: 907-923.
[128]Larissa Driemeier, Sergio P. Baroncini Proenc, Marcilio Alves. A contribution to the numerical nonlinear analysis of three-dimensional truss systems considering large strains, damage and plasticity [J]. Communications in Nonlinear Science and Numerical Simulation, 2005,10:515-535.
[129]T. Y. Yang, S. Saigal. A simple element for static and dynamic response of beams with material and geometric nonlinearities [J]. International Journal for Numerical Methods in Engineering,1984,20:851-867.
[130]N. Gebbeken. A refined numerical approach for the ultimate-load analysis of 3-D steel rod structures [J]. Engineering Computers,1998,15(3):312-344.
[131]W. S. King. A modified stiffness method for plastic analysis of semirigid frames [J]. Journal of Structural Division ASCE,1994,16(3):2156-2175.
[132]Afsin Saritas. Modeling of inelastic behavior of curved members with a mixed formulation beam element [J]. Finite Elements in Analysis and Design,2009,45:357-368.
[133]孙炳楠,洪涛,杨骊先.工程弹塑性力学[M].杭州：浙江大学出版社,2005.
[134]徐秉业,刘信声.应用弹塑性力学[M].北京：清华大学出版社,1995.
[135]W. J. Strong, T. X. Yu. Dynamic models for structural plasticity [M]. London: Springer-Verlag,1993.
[136]AASHTO. AASHTO LRFD Bridge Design Specification [S].1998.
[137]S. C. Tang, K. S. Yeung, C. T. Chon. On the tangent stiffness matrix in convected coordinate system [J]. Computers and Structures,1980,12:849-856.
[138]G. E. Blandford. Review of progressive failure analyses for truss structures [J]. Journal of Structure Engineering ASCE,1997,123(2):122-129.
[139]M. Papadrakakis. Inelastic post buckling analysis of trusses [J]. Journal of Structure Engineering ASCE,1983,109(9):2129-2147.
[140]C. D. Hill, G E. Blandford. Post-buckling analysis of steel space trusses [J]. Journal of Structure Engineering ASCE,1989,115(4):900-919.
[141]G. E. Blandford. Large deformation analysis of inelastic space truss structures [J]. Journal of Structure Engineering ASCE,1996,122(4):405-415.
[142]L. Kahn, R. Hanson. Inelastic cycle of axially loaded steel members [J]. Journal of Structure Engineering ASCE,1976,102(5):947-959.
[143]X. Q. Wu, C. Liu, T. X. Yu. A bifurcation phenomenon in an elastic-plastic symmetrical shallow truss subjected to a symmetrical load [J]. International Journal of Solids and Structures,1987,23(9):1225-1233.
[144]顾强.钢结构滞回性能及抗震设计[M].北京：中国建筑工业出版社,2009.
[145]朱世哲.双拱型空间钢管结构闸门的分析理论和试验研究杭州：浙江大学,2007.
[146]蔺海荣,冯维明,虞松.材料力学[M].北京：国防工业出版社,2001.
[147]Steen Krenk. Energy conservation in Newmark based time integration algorithms [J]. Computer Methods in Applied Mechanics and Engineeging,2006,195:6110-6124.
[148]J. M. Solberg, P. Papadopoulos. A finite element method for contact/impact [J]. Finite Elements in Analysis and Design,1998,1998(30):297-311.
[149]K. J. Bathe, P. A. Bouzinov. On the constraint function method for contact problems [J]. Computers and Structures,1997,64(5-6):1069-1085.
[150]凌道盛,徐兴.非线性有限元及程序[M].杭州：浙江大学出版社,2004.
[151]T. J. R. Hughes, R. L. Taylor, J. L. Sackman. A finite element method for a class of contact-impact problems [J]. Computer Methods in Applied Mechanics and Engineeging,1976, 8:249-276.
[152]A. B. Chaudhary, K. J. Bathe. A solution method for static and dynamic analysis of three-dimentional contact problems with friction [J]. Computers and Structures,1986,24: 855-873.
[153]J. T. Oden, N. Kikuchi. Finite element methods for constrained problems in elasticity [J]. International Journal for Numerical Methods in Engineering,1982,18:701-725.
[154]P. Papadopoulos, R. L. Taylor. A mixed formulation for the finite element solution of contact problems [J]. Computer Methods in Applied Mechanics and Engineeging,1992,94: 373-389.
[155]C. K. Choi, G. T. Chung. A gap element for three-dimensinal elasto-plastic contact problems [J]. Computers and Structures,1996,61(6):1155-1167.
[156]H. Schafer. A contribution to the solution of contact problems with the aid of bond elements [J]. Computer Methods in Applied Mechanics and Engineeging,1975,6:335-354.
[157]B. F. Maison, K. Kasai. Dynamics of pounding when two buildings collide [J]. Structures of Engineering ASCE,1992,21:771-786.
[158]吕林根,许子道.解析几何[M].北京：高等教育出版社,1987.
[159]J. A. Zukas, T. Nicholas, H. F. Swift, L. B. Greszczuk, D. R. Curran. Inpact dynamics [M]. New York:Wiley,1982.
[160]W. J. Stronge. Impact mechanics [M]. Cambridge, U. K.:Cambridge University Press, 2000.
[161]张雷明,刘西拉.钢筋混凝土结构倒塌分析的前沿研究[J].地震工程与工程振动,2003,23(3)：47-52.
[162]G. Kaewkulchai, E.B. Williamson. Modeling the Impact of failed members for progressive collapse analysis of frame structures [J]. Journal of Performance of Constructed Facilities ASCE,2006,20(4):375-383.
[163]赵凯华,罗蔚茵.新概念物理教程：力学[M].北京：高等教育出版社,2004.
[164]W. Goldsmith. Impact:The theory and physical behaviour of colliding solids [M]. London:Edword Arnold,1960.
[165]P. Wriggers, T. Vu Van, E. Stein. Finite element formulation of large deformation impact-contact problems with friction [J]. Computers and Structures,1990,37(3):319-331.
[166]欧进萍,段忠东,常亮.中国东南沿海重点城市台风危险性分析[J].自然灾害学报，2002,11(4)：9-17.
[167]曲晓宁,罗尧治,郑君华.悬挑网架在台风作用下的破坏机理研究[J].科技通报,2009,25(1)：77-82.
[168]中华人民共和国建设部.建筑结构荷载规范[S].北京,2002.