索拱结构体型及稳定性研究
|
摘要
拱结构具有良好的受力性能和审美价值,是被广泛应用的结构型式之一,但拱结构在反对称荷载作用下其受力性能较差,另外,拱结构支座的水平反力很大,要求下部支承结构有较大的水平刚度,而对于屋面结构满足此要求在实际工程中很难实现,索拱结构是拱与索的杂交结构,与无索拱相比其受力性能提高了很多,尤其是反对称荷载下更是如此,同时,其水平反力得到了控制。对于支座水平刚度要求的减少使得实际应用相当方便。本文对索拱结构进行了深入的研究,为该结构在实际工程中应用打下了坚实的基础。本文工作的具体内容有:
1、全面回顾了拱及其组合结构的结构形式以及索拱结构形式的来源、目前存在的问题和研究现状,并指出拱的组合结构以其良好的受力性能、审美价值以及丰富的组合形式是一种很有生命力的结构形式,在实际工程中具有广泛的应用前景。
2、索拱结构为大跨度柔性结构,只有用几何非线性分析方法对其稳定性研究,才可满足工程的实际需要,本文采用的几何非线性有限元方法是进行分析的更精确完善的力学模式,基于虚功原理,推导出了U.L.格式的空间梁元和索元的几何非线性有限元公式,采用Newton—Raphson法和弧长法求解了非线性平衡过程。
3、由于索拱结构中的矢跨比,荷载作用方式对索拱结构的稳定性起至关重要的作用,本文就六种索拱结构在不同矢跨比,及不同荷载作用方式下的特征值、极值荷载和整体刚度进行了讨论,就六种索拱结构的稳定性进行了对比研究。得到了每种索拱结构的受力性能。
With the characteristics of good load carring capacity and aesthetic feeling , arch structure has been widely used. But the arch structure has weakness in carring asymmetric load, especially having a large horizontal force in the skewback so that needing a large rigidity in the skewback support. But it is more difficult to meet the condition as a root structure. Compared with the arch structure, the cable-arch structure is improved greatly in earring load capacity, particularly in asymmetric load and decrease largely the horizontal force .For this reason, the cable-arch structure is consenienl for used in actual project. The behavior of cable-arch structure is studied in detail in this paper. The study lays solid theoretical foundations of applying the structure to actual projects.The relevant contents are as follows:1 The History、 study and problem of arch structure and arch composite structure at present is summarized in the paper. For the characteristics of good earring capacity、 aesthetic feeling and rich composite types , the arch composite structure would be widely used in actual project. The cable-arch structure is a kind of arch composite structure.2 The cable-arch structure is used often as a large span structure.Only using geometrical non-linearity to study the stability of the cable-arch structure can content the need of actual enginerring. A more perfect geometric nonliner mechanical mode is proposed here . Geometric nonlinear limit element method formulas of spatial beam
element and cable element are derrived. Geometric nonlinear equilibrium path is analyzed by Newton-Raphson Methed and Arch-length-type Method.3 Rise-span ratio and load action is important for the stability of cable-arch structure, The eigin, limit earring capacity and overall rigidity of six kinds of cable-arch structure are studied in different from rise-span ratio and load action, and the stability of the structures are comparatively studied so that the earring capacity of the six kinds of sturctures are obtained in the paper.4 Comparated with arch structure, the horizontal force is decreased largly in the cable-structure.The stability of six kinds of cable-arch structure are studied in defferent from sdewback anti-thrust rigidity and area of cross section of cable,when skewback anti-thrust rigity is small,the large earring capacity can be obtained in the structures. The capacity make it possible that the cable-arch structure can be used largly in actual project.5 A paraboloid cabe-arch structure and catenary cable-arch structure has not studied before.The stability of the structure is studied in defferent from load action n rise-span ratio ,area of cross section of cable and skewback anti-thrust rigidity. The study shows that the earring capacity is same as the cylindrical structure.6 For cable-arch stoucture can be used greatly in actual project, based on above work, a simple design method is developed for cable-arch structure.
1、全面回顾了拱及其组合结构的结构形式以及索拱结构形式的来源、目前存在的问题和研究现状,并指出拱的组合结构以其良好的受力性能、审美价值以及丰富的组合形式是一种很有生命力的结构形式,在实际工程中具有广泛的应用前景。
2、索拱结构为大跨度柔性结构,只有用几何非线性分析方法对其稳定性研究,才可满足工程的实际需要,本文采用的几何非线性有限元方法是进行分析的更精确完善的力学模式,基于虚功原理,推导出了U.L.格式的空间梁元和索元的几何非线性有限元公式,采用Newton—Raphson法和弧长法求解了非线性平衡过程。
3、由于索拱结构中的矢跨比,荷载作用方式对索拱结构的稳定性起至关重要的作用,本文就六种索拱结构在不同矢跨比,及不同荷载作用方式下的特征值、极值荷载和整体刚度进行了讨论,就六种索拱结构的稳定性进行了对比研究。得到了每种索拱结构的受力性能。
With the characteristics of good load carring capacity and aesthetic feeling , arch structure has been widely used. But the arch structure has weakness in carring asymmetric load, especially having a large horizontal force in the skewback so that needing a large rigidity in the skewback support. But it is more difficult to meet the condition as a root structure. Compared with the arch structure, the cable-arch structure is improved greatly in earring load capacity, particularly in asymmetric load and decrease largely the horizontal force .For this reason, the cable-arch structure is consenienl for used in actual project. The behavior of cable-arch structure is studied in detail in this paper. The study lays solid theoretical foundations of applying the structure to actual projects.The relevant contents are as follows:1 The History、 study and problem of arch structure and arch composite structure at present is summarized in the paper. For the characteristics of good earring capacity、 aesthetic feeling and rich composite types , the arch composite structure would be widely used in actual project. The cable-arch structure is a kind of arch composite structure.2 The cable-arch structure is used often as a large span structure.Only using geometrical non-linearity to study the stability of the cable-arch structure can content the need of actual enginerring. A more perfect geometric nonliner mechanical mode is proposed here . Geometric nonlinear limit element method formulas of spatial beam
element and cable element are derrived. Geometric nonlinear equilibrium path is analyzed by Newton-Raphson Methed and Arch-length-type Method.3 Rise-span ratio and load action is important for the stability of cable-arch structure, The eigin, limit earring capacity and overall rigidity of six kinds of cable-arch structure are studied in different from rise-span ratio and load action, and the stability of the structures are comparatively studied so that the earring capacity of the six kinds of sturctures are obtained in the paper.4 Comparated with arch structure, the horizontal force is decreased largly in the cable-structure.The stability of six kinds of cable-arch structure are studied in defferent from sdewback anti-thrust rigidity and area of cross section of cable,when skewback anti-thrust rigity is small,the large earring capacity can be obtained in the structures. The capacity make it possible that the cable-arch structure can be used largly in actual project.5 A paraboloid cabe-arch structure and catenary cable-arch structure has not studied before.The stability of the structure is studied in defferent from load action n rise-span ratio ,area of cross section of cable and skewback anti-thrust rigidity. The study shows that the earring capacity is same as the cylindrical structure.6 For cable-arch stoucture can be used greatly in actual project, based on above work, a simple design method is developed for cable-arch structure.
引文
[1] 沈祖炎,大跨空间结构的研究与发展,结构工程学的研究现状和趋势,同济大学出版社,1995,PP22-31.
[2] 林同炎,拱是结构也是建筑,土木工程学报,Vol.30,No.9,1997.
[3] 刘锡良,白正仙,张弦梁结构的有限元分析,空间结构,1998,4.
[4] 陆赐麟,预应力空间钢结构的现状和发展,空间结构,1994,1.
[5] 钟善桐,预应力钢结构。哈尔滨工业大学出版社,1986.
[6] 王新堂,预应力钢桁架刚度反演分析的摄动分析,计算力学学报,1999,16:(465-469).
[7] 沈祖炎,李元齐,‘新型大跨度空间结构形式—拱支网壳结构体系'、空间结构,1996,2(4):25-29.
[8] 陆赐麟,尹思明,刘锡良,现状应力钢结构,人民交通出版社,2003.
[9] 舒立茨,索贝克,哈伯曼著,殷福新等译,钢结构手册,大连理工大学出版社,2004
[10] 海诺·恩格尔著,林昌明等译,结构体系与建筑造型,天津大学出版社,2002
[11] 沈世钊,陈昕,林有军,汤建南,单层球面网壳的稳定性,空间结构,1997,3(3):3～12.
[12] 叶继红,沈祖炎,单层网壳结构在简单荷载下动力稳定分析,哈尔滨建筑大学学报,1997,30(1):24～31.
[13] 关富玲,高博青,李黎,单层网壳的稳定性分析,见:新型空间结构学术会议论文集,中国土木工程学会,1994.245～256.
[14] 刘承宗,赵惠麟,周志勇,单层组合网壳的双重非线性稳定问题,东南大学学报,1998,28(2):74～81.
15] 朱忠义、董石麟:单层穹顶网壳结构的几何非线性跳跃失稳及分岐屈曲的研究,空间结构,1995rh,1(2)期.
[16] 胡学仁,穹顶网壳的稳定理论和实验成果的若干回顾,空间网格结构论文集,同济大学出版社,1991,PP39-53.
[17] 项海帆,刘光栋,拱结构的稳定与振动.人民交通出版社.1986.
[18] 罗永峰,网壳结构弹塑性稳定及承载全过程研究,同济大学博士论文,1991.
[19] 沈世钊,陈昕,网壳结构稳定性,科学出版社,1999.
[20] 胡学仁,穹顶网壳的稳定计算,第四届空间结构学术会议论文集,P525-536.
[21] 胡学仁等,穹顶网壳的稳定性和非稳定性特性的实验研究,空间网格结构论文集,pp54-60.
[22] 钱若军,李亚玲,网壳结构非线性稳定分析研究,空间网格结构论文集,pp61-68.
[23] 林有军,沈世钊,K6型单层球面网壳结构的稳定性,哈尔滨建筑大学学报,1997,28(增刊):115～118.
[24] 刘古岷,张若晞,张田申,应用结构稳定计算,科学出版社,2004.
[25] 陈骥,钢结构稳定理论与设计,科学出版社,2001.
[26] 吕烈武,沈世剑,沈祖炎,胡学仁,钢结构构件稳定理论,中国建筑工业出版社,1983.
[27] 沈祖炎、罗永峰:网壳结构分析中节点大位移迭加及平衡路跟踪技术的修正,新型空间结构论文集,浙江大学出版社,1994年.
[28] 陈昕,沈世钊,单层穹顶网壳的荷载—位移全过程及缺陷分析,建筑结构学报,13(3),1992,PP11-18.
[29] 王晓波,索拱结构的理论分析、试验研究及工程应用,天津大学硕士研究生毕业论文,2000,3.
[30] 王勖成,邵敏,有限单元基本原理和数值方法,清华大学出版社,1995.105～150.
[31] 陈政清,曾庆元,颜全胜:空间杆系结构大挠度问题内力分析的UL列式法,土木工程学报,Vol.25,No.5,1992。
[32] 蒋友谅,非线性有限元法,北京工业学院出版社,1988.
[33] 白正仙,张弦梁结构的理论分析与试验研究,天津大学博士研究生毕业论文,1999,1.
[34] 孙建恒,赵惠麟,单层穹顶网壳的后屈曲分析及试验研究,空间网格结构论文集,pp69-77.
[35] 曹国中,赵惠麟,单层球形网壳的弹性屈曲分析及其试验研究,空间网格结构论文集,PP78-88.
[36] 黄为民、赵惠麟,具有随机何缺陷的单层网壳监界荷载的确定;空间结构,1994,1(2)pp26-32.
[37] 李元齐、大跨度拱支网壳结构的稳定性研究,同济大学博士论文,1998.
[38] 孙剑辉,胡学仁,网壳的几何缺陷对其稳定性影响的研究,第六届空间结构学术会议论文集,1992.12.广州.pp455-462.
[39] 钱若军,网壳结构设计监界荷载及安全系数,建筑结构学报,1995,16(3)pp44-51.
[40] 沈世钊,陈昕,网壳结构的几何非线性分析,土木工程学报,1990年,23(3),47～57.
[41] 夏绍华,钱若军,网壳结构非线性稳定分析中屈曲类型的判别。见:新型空间结构论文集,中国土木工程学会,1992.177～185.
[42] 钱若军,沈祖炎,夏绍华,网壳结构失稳机理及分析模型的研究,见:新型空间结构论文集,中国土木工程学会,1992.170～176.
[43] 黄为民,赵惠麟,具有缺陷单层网壳稳定性的模型实验研究与分析,见:新型空间结构论文集,中国土木工程学会,1994.151～159.
[44] 孙剑辉,胡学仁,网壳的几何缺陷对其稳定性影响的研究,见:新型空间结构论文集,中国土木工程学会,1994.230～237.
[45] 张峰,沈世钊,魏昕,初始缺陷对单层柱面网壳稳定性的影响,哈尔滨建筑大学学报,1997,30(6):36～42.
[46] 夏绍华,钱若军,网壳结构非线性分析力学模型研究,1994,见:新型空间结构论文集,中国土木工程学会,1994.134～143.
[47] 马军,赵惠麟,赵才其,单层组合网壳的弹塑性分析及实验研究,东南大学学报,1996年11月26(11):87～93.
[48] 王娜,陈昕,沈世钊,网壳结构弹塑性大位移全过程分析,土木工程这报,1993,26(2):19～27.
[49] 罗永峰,沈祖炎,胡学仁,单层网壳结构弹塑性稳定实验研究,新型空间结构论文集,1994.中国土木工程学会,1994.194～201.
[50] 罗永峰,沈祖炎,胡学仁,单层网壳结构弹塑性稳定实验研究,新型空间结构论文集,中国土木工程学会,1994.202～208.
魏德敏,拱的非线性理论及其应用,科学出版社,2004
[51] Tokarz F.J., Sandhu R.S.Lateral-tortional buckling of parabolic arches.Journal of Structural Engineering, 1972,98(5): 1161~1179.
[52] Wen R.K.,Lange J.Curved beam elemint for arch buckling analysis.Journal of Structural Engineering,1981,107(11):174~183.
[53] F.Otto,Tensile structures,Cambridge, 1973,Vol.1.
[54] Chini S. A, Wolde-Tinsae A. M. Critical load and postbuckling of arch framework. Journal of Engineering Mechanics ,1988,114(9):1435~1453.
[55] KeeC. F. Lateral inelastic buckling of tied arch.journal of Structural Engineering,1961,87(1):23~29.
[56] Komatsu S, Sakimoto T . Ultimate load carrying capacity of steel arches. Journal of Structural Engineering ,1997,103(12):2323~2336.
[57] Paoanjilis J.p., Trahair N.S.Flexual tortional buckling of arches. Journal of Structural Engineering, 1987,113(4):889~906.
[58] Paoanjilis J.P.,Trahair N.S. Finite element analysis of arch lateral buckling. Civil Engineering Trans.,1987,CE29(1):34~39.
[59] Sakimoto T., Kumatsu S . Ultimate Strength formula for steel arches. Journal of Structural Engineering, 1983,109(3):613~627.
[60] Pi Y. L, Trahair N .S. In-plane inelastic lateral buckling strength and design of steel arches. Engineering Structure,2000,22:993~1005.
[61] Pi Y. L, Trahair N. S. In-plane inelastic buckling and strength of steel arches. Journal of Structural Engineering,1996,122(7),734~747.
[62] Pi Y. L, Trahair N S.Non-lineart buckling and postbuckling of elastic arches. Engineering Structure, 1998,20(7),571 ~579.
[63] Pi Y. L, Trahair N. S. Out-of-plane inelastic buckling and strength of steel arches. Journal of Structural Engineering, 1998,125(2): 174~183.
[64] Pi Y. L, Trahair N. S.In-plane buckling and design of steel arches. Journal of Structural Engineering, 1999,125(11):1291 ~1298.
[65] Gioncu V. Buckling of reticulated shells:state of the art. Journal of Space Structures, 1995,10( 1): 1 ~45.
[66] Nie G.H., Cheung Y.K. A.nonlinear model for stability analysis of reticulated shallow shells with imperfections.Journal of Space Structures, 1995,8(4):215~ 230.
[67] Takashima H .,Kato S . Numerical simulation of elastic-plastic buckling behaviour of a reticular dome,Journal of Space structure,1993,8(4):1314~1322.
[68] T.See,R.E.Meconnell,Large Displacement Elastic Buckling of Space Frames,J.Struct.Engng.,Vo. 112,No.5,1986,PP1052-1069.
[69] J.Chrescielewski&R. Schmiot: A Solution Control Method for Nonlinear Finite Element Post-Buckling Analysis of Structures,Post-Buckling of Elastic Structures Proceeding of the Euromech Colloquium,Edited by Z.S. Gaspar,1985.
[70] Victor Gioncu,Buckling of Reticulated Shells: State-of-the-Art, International Journal of Soace Structures, Vol. 10No.1,1995,PP1-46.
[71] Sxilard R.,Critical Load Post-buckling Analysis by FEM Using Energy Balancing Technique, Computers&Structures, Vol. 20,1985, PP277~286.
[72] P Sharifi,E P Popov. Nonlinear buckling analysis of sandwich arches. J. Eng. Mech.,Div.,Vol.97,1971,ppl397-1412.
[73] Feng Y.T Peric D.& Owen D.R.J., A new eriterion for determination of initial loading parameter in arc-length methods, Comp.& Struct., 1996, 58:479-485.
[74] Fafard M.& Massicotte B., Geometrical interpretation of the arc-length method,Comp.&Struct., 1993,46:608-615.
[75] Matushita F.,OHYA T.Mukaiyana Y., Matsue Y.Study of the esasto-plastic bulking of single-layer domes.Space Structures, Thomas Telford, London, 1993,10(4): 167~175.
[76] Du S., Sun J., Xia H.Stability behaviour investigation of braced barrel vaults,Space Structures,Thomas Telford,London,1993,8(4):62~68.
[77] SUMEC J.Some stability aspects of reticulated shells,Space Structures4.Thomas Telford,London,1993,8(4):339~346.
[78] Mudaiyama Y, Uedi T.Lato S., and Kubodela I.Study on elasto-plastic dynamic bulkling behavior of high-rise single layered domeds.IASS,1990,12(6):689~697.
[79] Chen W.F., Goto Y, Richard J.Y.Stability design of semi-rigid frames.USA:Jhn Wiley&Sons,1996.
[80] Ziemian R.D.,McGuire W.,Deierlien G, Inelastic limit states design.Part I:Planar frame studies.Journal of the Structural Engineering,1992,118(9):2532-2549.
[81] Chen H., Blandford G.E.Working-increment-control methods for nonlinear analysis. Journal of Numerical Methods in Engineering, 1993, 36:909-930.
[82] Yang Y.B., Yau Y.D.Stability of beams with tapered I-sections. Journal of Engineering Mechanics, 1987,113(9): 1337-1357.
[83] Just.D.J.Plane Frameworks of tapering box and I-section.Journal of Structural Engineering. 1977,103(1):71-86.
[84] Crisfield.M.A.A Fast incremental/iterative solution procedure that handles "Snap-Through".Computers&Structures, 1981,13:55-62.
[85] Riks.E$.An Incremental approach to the solution of snapping and buckling problems.International Journal of Solids Structures, 1979,15:529-551.
[86] Faris GA.Al-Bermani,S.Kitipornchai.Elasto-plastic large deformation analysis of thin-walled structures.Engineering Structures, 1990,12 : 28-36.
[87] Johnston B.G,Cheney zl.Steel columns of rolled wide flange section.Progress Report No.2,American Institute of Steel Construction. 1942-11.
[88] Breadford M.A.Inelastic distortional buckling of I-beams. Computer & Structure, 1986,24(6):923~933.
[89] Breadford M.A.Distortional instability of fabricated monosymmetric I-beams. Computer & Structure, 1986,29(4):715-724.
[90] Cook R.D.On the Allman triangle and a related quadrilateral elenent. Computer & structure, 1986,22:1065~1076.
[91] Yunus S.M.A study of different hybrid elenent with and without rotational DOF For plane stress/plane strain problems. Computer & Strucure, 1988,30;l 127~1130.
[92] T.Belytschko&L.Glaum,Application of higher order corotational stretch theories to nonlinear finite element analysis,Comp.& Struct., 1980,10:175-182.
[93] E.Riks.An inerenental approach to the solution of snapping and buckling problems,Int.J.Solids.Struct., 1979,15:529-551:
[94] Pwriggers&J.C.Simo,Ageneral procedure for the direct computation of turning and bifurcation points, Int.J.Num. Meth.Engng., 1990, 30: 155-176.
[95] KJ.Bathe & A.P.Cimento,Some practical procedures for the solution of nonlinear finite elenent equations,Comp.,Methods Appl. engng., 1980,22: 59-85.
[96] A.K.Noor&J.M.Peters,Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams, Int.J. Num. Meth. Engng.,1981,17:615-631.
[97] T.belytschdo,L.Schwer & M.J.Klein,Large displacement transient analysis of space frames,Int.J.Num.Meth.Engng.,1977.11:65-84.
[98] j.l.Meek&S.Loganathan:Large Displacement Analysis of Space-Frame Structures, Computer Methods in Applied Mechanics and Engineering, 1989, Vol.72, pp.57-75.
[99] Masahisa Fujikake:A Simple Approach to Bifurcation and limit Point Calculations, Intenational Jounal for Nrmerical Methods in Engineering, 1985, Vol.21, pp.183-191.
[100] J. Chrescielewski&R.Schmot:A Solution Control Method for Nonlinear Finite Element Post-Buckling Analysis of Structures,Post-Buckling of Elastic Structures,Proceeking of the Euromech Colloquium ,Edited byZ.S. Gaspar, 1985.
[101] Rasmussen K.J.R.Bifurcation of locally buckled members. Thin-walled Structure, 1997,28(2), 117~154.
[102] Pi Y. L, Trahair N. S.Nonlinear inelastic analysis of steel beam-columns. II: Application. Journalof Structural Engineering, 1994 ,120(7):2062~2085.
[103] Pi Y. L, Trahair N. S.Nonlinear inelastic analysis of steel beam-columns. I;theory. Journal of Structural Engneering, 1994,120 (7): 2041~2061.
[104] Fathelbab F.A.,Tangent stiffness matrix for space frame members with both member and joint imperfections. Space Structures4.Thomas Telford, London, 1993,10(4):1323~1333.
[105] Dubina D.,Computation Models and Numerical Solution Procedures for Nonlinear of Single Layer Lattice Shells,International Joural of Space Structure, Vol.8,No.3,1993,PP321~333.
[106] GShi&S.N.Atluri,Elasto-plastic large Deformation Analysis of Space-Frames:A Plastic-Hinge and Stress-based Explicit Derivation of Tangent Stiffnesses, Internation Journal for Numerical methods in Engineering, Vo.26, 1988, PP589-615.
[107] J.H.Argyris,B.Borri,V.Hindenlang,M.Kleiber,Finite Element Analysis of Two-And Three-Dimensional Elasto-Plastic Frames—The Natural Approach, Comput. Meth.for Appl.Mech.Engng.,Vo.35,1982,PP221 -248.
[108] T See, R E Mcconnell. Large displacement elasic buckling of space structures. J. Struct. Engng,Vol.112,No.5,1986,PP1052-1069.
[109] E Riks. An incremental approach to the solution of snapping and buckling problems. Int.J.Solids Structures,Vo115,1979,pp529-551.
[110] M A Crisfield. An arc-length method including line searches and accelerations. Int.J. of Num. Mech.Eng.,Vo119,1983,pp1269-1289.
[111] R.D wood,O.C. Zienkiewicz,Geometrically nonlinear finite element analysis of beams,frames, arches and axisymmetric shells,Comp.and Struct,Vol.7,1977.
[112] Yang Y.B.,Kuo S.R.Theory& Analysis of nonlinear framed structures.Prentice Hall: 1994.170~234.
[113] Wang N.,Chen X., Shen S. Z. Geometric and material nonlinear analysis of latticed shells of negative Gaussoan curvature, Space Structures. Thomas Telford, London, 1993., 10 (4) : 649 ~ 654.
[114] Yamashita T., Kunieda H.Geometrical Nonlinear Analsis of Single -layer Latticed Dome. IASS, 1990 ,12(6):476~509.
[115] Choong K.K., Hangai Y.Review on methods of bifurcation analysis for geometrically nonlinear structure.Bulletin of the IASS, 1993, 34, 133-149.
[116] Clarke M.J.,Hancock Y.A study of increment-iterative strategies for nonlinear ananlyses.Journal of Numerical Methods in Engineering, 1990, 29: 1365~1391.
[117] Ramm.E.Strategies for Tracing the non-linear response near limit points.In:Wunderlich W,Stein E and Bathe KJ eds.Non-Linear Finite Elenent Analysis in Structural Mechanics,1981:63-89.
[118] Theodore V.Galambos,Robert L.Ketter.Columns under combined bending and thrust. Journal of Engineering Mechanics Division, 1959, 85(2): 1-30
[119] J.H.Argyris,An excursion into large rotations, Comp. Meth. Appl, Mech, Engng., 1982,32:85-155.
[120] R.B.Fuller,Non-symmetrical tension-integrity structures, U.S. Patent, Aug. 7,1973,No.3866366.
[121] Sleeb A.F.,Gendy A.S. Shear-flexible models for spatial bucking of thin-walled curved beams.Journal of Numerical Methods in Engineering. 1991,31(4): 729 ~ 759.
[122] Chen W.F.,Kim S .E.LEFD steel design using advanced analysis .CRC Press: 1997.
[123] J.L.Meek,H.S.Tan,Geometrically Non-Linear Analysis of Space Frames by An Incremental Iterative, Comput. Meth. forAppl. Mech. Engng., Vo.47, 1984, PP261-282.
[124] R.Srilard,Critical Load and Post-Buckling Analysis of Space Frames by Finite Element Method Using Energy Balancing Technique, Comput.Struct.,Vo. 20, No.l-3,1985,PP277-286.
[125] F.S. William, An approach to the nonlinear behaviour of the members of a rigid jointed plane framework with finite element deflections,.J. MechAppl. Math., Val.17,1964.
[126] R.K. Wen, Nonlinear elastic frame analysis by finite element,J Struct. Eng., Vol.109,1983.
[127] J.Jconnor.R.D.Logcher&S.C.Chan,Nonlinear analysis of elastic framed structures, J.Struct.Div, ASCE1968,94,1525~1547.
[128] B.A.Schrefler&S. A total lagrangian geometrically non-linear analysisof combined beam and cable structures,Comp & Struct, 1983 ,17:115-127.
[129] Zhang Qilin,Ineremental finite element solution for nonlinear problems of space truss,J.Construct.Steel Research, 19961,20:89-104.
[130] R.K.Wen &J.Rahimzadeh,Nonlinear finite elastic frame analysis by finite element,J.Struct.Engng.,ASCE,1983,109:1952-1971.
[131] K.J.Bathe & S.Bolourchi,Large displacement analysis of three- dimensional beam structures,Int.J.Num.Meth.Engng., 1979,14:961 -989.
[132] E.Riks,The application of Newton's method to the problem of elastic stability,J. Appl.Mech.,1972,39:1060-1066.
[133] M.A.Crisfield,A fast incremental/iterative solution procedure that handles "snap-through",Comp.& Struct., 1981,13:55-62.
[134] M.A.Crisfied,An arc-length method including line searehes and accelerations,Int.J.Num.Meth.Engng., 1983,19:1269-1289.
[135] M.A.Clarke &GJ.hancock,A study of incremental-iterative strategies for non-linear analysis, Int. J. Num. Meth, Engng, 1990,29 : 1365 -1391.
[136] Lind N.C.Local instability analysis of triangulated dome frameworks. The Structure Engeneer, 1969,47(8) :317 ~ 324.
[137] White D.W.Plastic-hinge methods for advanced analysis of steel frames. Journal of the Construction Steel Research,1993,24:121~152.
[138] White D.W.,Richard J.Y.,Chen W.F.Second-order inelastic analysis for frame design:A report to SSRC task group 29 on recent research and the perceived state-of-the-Art,Structural Engineering CE- STR- 91- 12, School of Civil Engineering,Purdue University, 1991.
[139] King W.S., White D.W., Chen W.F.Second order inelastic analysis methods for steel-frame design. Journal of Structural Engineering, 1992,118(2): 408-428.
[140] Orbison J.G, McGuire W.,Abel J.F.Yield surface applications in nonlinear steel frame analysis.Computer Methods in Applied Mechanics and Engineering, 1982,33:557-573.
[141] Ziemian R.D., McGuire W., Deierlien G.Inelestic limit states design.Part II: Three-dimensionla frame studies. Journal of the Structural Engineering, 1992, 118(9):2550-2568
[142] Richard J.Y., Whete D.W., Chen W.F.Second-order refined plastic-hinge analysis for frame design.Part I.Journal of Structural Engineering, 1993, 119(11): 3196-3216.
[143] White D.W.Material and Geometric Nonlinear analysis of local planar behavior in steel frames using interactive computer graphics:MS Thesis,Cornell Univ., Ithaca,N.Y1985.
[144] Chen W.F,Atsuta T.Theory of beam-columns.Volume 1:In-plane behavior and design.New York:McGraw-Hill,1976.
[145] Chen W.F,Atsuta T.Theory of beam-columns.Volume 2:Space behavior and design.New York:McGraw-Hill,1976.
[146] Al-Mashary F., Chen W.F. Simplified second-order inelastic analysis for steel frames.The Structural Engineer, 1991,69(23):395-399.
[147] King W.S.A Modified stiffness method for plastic analysis of steel frames.Engineering Structures, 1994,16(3): 162-170.
[148] Richard J.Y., White D.W,Chen W.F.Notional-load plastic-hinge method for frame design, Journal of Structural Engineering, 1994,120 (5): 1434-1454.
[149] Duan L., Chen W.F.Design interaction equation for steel beam-columns.Journal of Structural Engineering, 1989,115(5): 1225-1243. 150 、 Zhou S.P.,Duan L.,Chen W.F. Comparison of design equations for steel beam-columns. Structural Engineering Review, 1990,2(1):45-53
[2] 林同炎,拱是结构也是建筑,土木工程学报,Vol.30,No.9,1997.
[3] 刘锡良,白正仙,张弦梁结构的有限元分析,空间结构,1998,4.
[4] 陆赐麟,预应力空间钢结构的现状和发展,空间结构,1994,1.
[5] 钟善桐,预应力钢结构。哈尔滨工业大学出版社,1986.
[6] 王新堂,预应力钢桁架刚度反演分析的摄动分析,计算力学学报,1999,16:(465-469).
[7] 沈祖炎,李元齐,‘新型大跨度空间结构形式—拱支网壳结构体系'、空间结构,1996,2(4):25-29.
[8] 陆赐麟,尹思明,刘锡良,现状应力钢结构,人民交通出版社,2003.
[9] 舒立茨,索贝克,哈伯曼著,殷福新等译,钢结构手册,大连理工大学出版社,2004
[10] 海诺·恩格尔著,林昌明等译,结构体系与建筑造型,天津大学出版社,2002
[11] 沈世钊,陈昕,林有军,汤建南,单层球面网壳的稳定性,空间结构,1997,3(3):3～12.
[12] 叶继红,沈祖炎,单层网壳结构在简单荷载下动力稳定分析,哈尔滨建筑大学学报,1997,30(1):24～31.
[13] 关富玲,高博青,李黎,单层网壳的稳定性分析,见:新型空间结构学术会议论文集,中国土木工程学会,1994.245～256.
[14] 刘承宗,赵惠麟,周志勇,单层组合网壳的双重非线性稳定问题,东南大学学报,1998,28(2):74～81.
15] 朱忠义、董石麟:单层穹顶网壳结构的几何非线性跳跃失稳及分岐屈曲的研究,空间结构,1995rh,1(2)期.
[16] 胡学仁,穹顶网壳的稳定理论和实验成果的若干回顾,空间网格结构论文集,同济大学出版社,1991,PP39-53.
[17] 项海帆,刘光栋,拱结构的稳定与振动.人民交通出版社.1986.
[18] 罗永峰,网壳结构弹塑性稳定及承载全过程研究,同济大学博士论文,1991.
[19] 沈世钊,陈昕,网壳结构稳定性,科学出版社,1999.
[20] 胡学仁,穹顶网壳的稳定计算,第四届空间结构学术会议论文集,P525-536.
[21] 胡学仁等,穹顶网壳的稳定性和非稳定性特性的实验研究,空间网格结构论文集,pp54-60.
[22] 钱若军,李亚玲,网壳结构非线性稳定分析研究,空间网格结构论文集,pp61-68.
[23] 林有军,沈世钊,K6型单层球面网壳结构的稳定性,哈尔滨建筑大学学报,1997,28(增刊):115～118.
[24] 刘古岷,张若晞,张田申,应用结构稳定计算,科学出版社,2004.
[25] 陈骥,钢结构稳定理论与设计,科学出版社,2001.
[26] 吕烈武,沈世剑,沈祖炎,胡学仁,钢结构构件稳定理论,中国建筑工业出版社,1983.
[27] 沈祖炎、罗永峰:网壳结构分析中节点大位移迭加及平衡路跟踪技术的修正,新型空间结构论文集,浙江大学出版社,1994年.
[28] 陈昕,沈世钊,单层穹顶网壳的荷载—位移全过程及缺陷分析,建筑结构学报,13(3),1992,PP11-18.
[29] 王晓波,索拱结构的理论分析、试验研究及工程应用,天津大学硕士研究生毕业论文,2000,3.
[30] 王勖成,邵敏,有限单元基本原理和数值方法,清华大学出版社,1995.105～150.
[31] 陈政清,曾庆元,颜全胜:空间杆系结构大挠度问题内力分析的UL列式法,土木工程学报,Vol.25,No.5,1992。
[32] 蒋友谅,非线性有限元法,北京工业学院出版社,1988.
[33] 白正仙,张弦梁结构的理论分析与试验研究,天津大学博士研究生毕业论文,1999,1.
[34] 孙建恒,赵惠麟,单层穹顶网壳的后屈曲分析及试验研究,空间网格结构论文集,pp69-77.
[35] 曹国中,赵惠麟,单层球形网壳的弹性屈曲分析及其试验研究,空间网格结构论文集,PP78-88.
[36] 黄为民、赵惠麟,具有随机何缺陷的单层网壳监界荷载的确定;空间结构,1994,1(2)pp26-32.
[37] 李元齐、大跨度拱支网壳结构的稳定性研究,同济大学博士论文,1998.
[38] 孙剑辉,胡学仁,网壳的几何缺陷对其稳定性影响的研究,第六届空间结构学术会议论文集,1992.12.广州.pp455-462.
[39] 钱若军,网壳结构设计监界荷载及安全系数,建筑结构学报,1995,16(3)pp44-51.
[40] 沈世钊,陈昕,网壳结构的几何非线性分析,土木工程学报,1990年,23(3),47～57.
[41] 夏绍华,钱若军,网壳结构非线性稳定分析中屈曲类型的判别。见:新型空间结构论文集,中国土木工程学会,1992.177～185.
[42] 钱若军,沈祖炎,夏绍华,网壳结构失稳机理及分析模型的研究,见:新型空间结构论文集,中国土木工程学会,1992.170～176.
[43] 黄为民,赵惠麟,具有缺陷单层网壳稳定性的模型实验研究与分析,见:新型空间结构论文集,中国土木工程学会,1994.151～159.
[44] 孙剑辉,胡学仁,网壳的几何缺陷对其稳定性影响的研究,见:新型空间结构论文集,中国土木工程学会,1994.230～237.
[45] 张峰,沈世钊,魏昕,初始缺陷对单层柱面网壳稳定性的影响,哈尔滨建筑大学学报,1997,30(6):36～42.
[46] 夏绍华,钱若军,网壳结构非线性分析力学模型研究,1994,见:新型空间结构论文集,中国土木工程学会,1994.134～143.
[47] 马军,赵惠麟,赵才其,单层组合网壳的弹塑性分析及实验研究,东南大学学报,1996年11月26(11):87～93.
[48] 王娜,陈昕,沈世钊,网壳结构弹塑性大位移全过程分析,土木工程这报,1993,26(2):19～27.
[49] 罗永峰,沈祖炎,胡学仁,单层网壳结构弹塑性稳定实验研究,新型空间结构论文集,1994.中国土木工程学会,1994.194～201.
[50] 罗永峰,沈祖炎,胡学仁,单层网壳结构弹塑性稳定实验研究,新型空间结构论文集,中国土木工程学会,1994.202～208.
魏德敏,拱的非线性理论及其应用,科学出版社,2004
[51] Tokarz F.J., Sandhu R.S.Lateral-tortional buckling of parabolic arches.Journal of Structural Engineering, 1972,98(5): 1161~1179.
[52] Wen R.K.,Lange J.Curved beam elemint for arch buckling analysis.Journal of Structural Engineering,1981,107(11):174~183.
[53] F.Otto,Tensile structures,Cambridge, 1973,Vol.1.
[54] Chini S. A, Wolde-Tinsae A. M. Critical load and postbuckling of arch framework. Journal of Engineering Mechanics ,1988,114(9):1435~1453.
[55] KeeC. F. Lateral inelastic buckling of tied arch.journal of Structural Engineering,1961,87(1):23~29.
[56] Komatsu S, Sakimoto T . Ultimate load carrying capacity of steel arches. Journal of Structural Engineering ,1997,103(12):2323~2336.
[57] Paoanjilis J.p., Trahair N.S.Flexual tortional buckling of arches. Journal of Structural Engineering, 1987,113(4):889~906.
[58] Paoanjilis J.P.,Trahair N.S. Finite element analysis of arch lateral buckling. Civil Engineering Trans.,1987,CE29(1):34~39.
[59] Sakimoto T., Kumatsu S . Ultimate Strength formula for steel arches. Journal of Structural Engineering, 1983,109(3):613~627.
[60] Pi Y. L, Trahair N .S. In-plane inelastic lateral buckling strength and design of steel arches. Engineering Structure,2000,22:993~1005.
[61] Pi Y. L, Trahair N. S. In-plane inelastic buckling and strength of steel arches. Journal of Structural Engineering,1996,122(7),734~747.
[62] Pi Y. L, Trahair N S.Non-lineart buckling and postbuckling of elastic arches. Engineering Structure, 1998,20(7),571 ~579.
[63] Pi Y. L, Trahair N. S. Out-of-plane inelastic buckling and strength of steel arches. Journal of Structural Engineering, 1998,125(2): 174~183.
[64] Pi Y. L, Trahair N. S.In-plane buckling and design of steel arches. Journal of Structural Engineering, 1999,125(11):1291 ~1298.
[65] Gioncu V. Buckling of reticulated shells:state of the art. Journal of Space Structures, 1995,10( 1): 1 ~45.
[66] Nie G.H., Cheung Y.K. A.nonlinear model for stability analysis of reticulated shallow shells with imperfections.Journal of Space Structures, 1995,8(4):215~ 230.
[67] Takashima H .,Kato S . Numerical simulation of elastic-plastic buckling behaviour of a reticular dome,Journal of Space structure,1993,8(4):1314~1322.
[68] T.See,R.E.Meconnell,Large Displacement Elastic Buckling of Space Frames,J.Struct.Engng.,Vo. 112,No.5,1986,PP1052-1069.
[69] J.Chrescielewski&R. Schmiot: A Solution Control Method for Nonlinear Finite Element Post-Buckling Analysis of Structures,Post-Buckling of Elastic Structures Proceeding of the Euromech Colloquium,Edited by Z.S. Gaspar,1985.
[70] Victor Gioncu,Buckling of Reticulated Shells: State-of-the-Art, International Journal of Soace Structures, Vol. 10No.1,1995,PP1-46.
[71] Sxilard R.,Critical Load Post-buckling Analysis by FEM Using Energy Balancing Technique, Computers&Structures, Vol. 20,1985, PP277~286.
[72] P Sharifi,E P Popov. Nonlinear buckling analysis of sandwich arches. J. Eng. Mech.,Div.,Vol.97,1971,ppl397-1412.
[73] Feng Y.T Peric D.& Owen D.R.J., A new eriterion for determination of initial loading parameter in arc-length methods, Comp.& Struct., 1996, 58:479-485.
[74] Fafard M.& Massicotte B., Geometrical interpretation of the arc-length method,Comp.&Struct., 1993,46:608-615.
[75] Matushita F.,OHYA T.Mukaiyana Y., Matsue Y.Study of the esasto-plastic bulking of single-layer domes.Space Structures, Thomas Telford, London, 1993,10(4): 167~175.
[76] Du S., Sun J., Xia H.Stability behaviour investigation of braced barrel vaults,Space Structures,Thomas Telford,London,1993,8(4):62~68.
[77] SUMEC J.Some stability aspects of reticulated shells,Space Structures4.Thomas Telford,London,1993,8(4):339~346.
[78] Mudaiyama Y, Uedi T.Lato S., and Kubodela I.Study on elasto-plastic dynamic bulkling behavior of high-rise single layered domeds.IASS,1990,12(6):689~697.
[79] Chen W.F., Goto Y, Richard J.Y.Stability design of semi-rigid frames.USA:Jhn Wiley&Sons,1996.
[80] Ziemian R.D.,McGuire W.,Deierlien G, Inelastic limit states design.Part I:Planar frame studies.Journal of the Structural Engineering,1992,118(9):2532-2549.
[81] Chen H., Blandford G.E.Working-increment-control methods for nonlinear analysis. Journal of Numerical Methods in Engineering, 1993, 36:909-930.
[82] Yang Y.B., Yau Y.D.Stability of beams with tapered I-sections. Journal of Engineering Mechanics, 1987,113(9): 1337-1357.
[83] Just.D.J.Plane Frameworks of tapering box and I-section.Journal of Structural Engineering. 1977,103(1):71-86.
[84] Crisfield.M.A.A Fast incremental/iterative solution procedure that handles "Snap-Through".Computers&Structures, 1981,13:55-62.
[85] Riks.E$.An Incremental approach to the solution of snapping and buckling problems.International Journal of Solids Structures, 1979,15:529-551.
[86] Faris GA.Al-Bermani,S.Kitipornchai.Elasto-plastic large deformation analysis of thin-walled structures.Engineering Structures, 1990,12 : 28-36.
[87] Johnston B.G,Cheney zl.Steel columns of rolled wide flange section.Progress Report No.2,American Institute of Steel Construction. 1942-11.
[88] Breadford M.A.Inelastic distortional buckling of I-beams. Computer & Structure, 1986,24(6):923~933.
[89] Breadford M.A.Distortional instability of fabricated monosymmetric I-beams. Computer & Structure, 1986,29(4):715-724.
[90] Cook R.D.On the Allman triangle and a related quadrilateral elenent. Computer & structure, 1986,22:1065~1076.
[91] Yunus S.M.A study of different hybrid elenent with and without rotational DOF For plane stress/plane strain problems. Computer & Strucure, 1988,30;l 127~1130.
[92] T.Belytschko&L.Glaum,Application of higher order corotational stretch theories to nonlinear finite element analysis,Comp.& Struct., 1980,10:175-182.
[93] E.Riks.An inerenental approach to the solution of snapping and buckling problems,Int.J.Solids.Struct., 1979,15:529-551:
[94] Pwriggers&J.C.Simo,Ageneral procedure for the direct computation of turning and bifurcation points, Int.J.Num. Meth.Engng., 1990, 30: 155-176.
[95] KJ.Bathe & A.P.Cimento,Some practical procedures for the solution of nonlinear finite elenent equations,Comp.,Methods Appl. engng., 1980,22: 59-85.
[96] A.K.Noor&J.M.Peters,Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams, Int.J. Num. Meth. Engng.,1981,17:615-631.
[97] T.belytschdo,L.Schwer & M.J.Klein,Large displacement transient analysis of space frames,Int.J.Num.Meth.Engng.,1977.11:65-84.
[98] j.l.Meek&S.Loganathan:Large Displacement Analysis of Space-Frame Structures, Computer Methods in Applied Mechanics and Engineering, 1989, Vol.72, pp.57-75.
[99] Masahisa Fujikake:A Simple Approach to Bifurcation and limit Point Calculations, Intenational Jounal for Nrmerical Methods in Engineering, 1985, Vol.21, pp.183-191.
[100] J. Chrescielewski&R.Schmot:A Solution Control Method for Nonlinear Finite Element Post-Buckling Analysis of Structures,Post-Buckling of Elastic Structures,Proceeking of the Euromech Colloquium ,Edited byZ.S. Gaspar, 1985.
[101] Rasmussen K.J.R.Bifurcation of locally buckled members. Thin-walled Structure, 1997,28(2), 117~154.
[102] Pi Y. L, Trahair N. S.Nonlinear inelastic analysis of steel beam-columns. II: Application. Journalof Structural Engineering, 1994 ,120(7):2062~2085.
[103] Pi Y. L, Trahair N. S.Nonlinear inelastic analysis of steel beam-columns. I;theory. Journal of Structural Engneering, 1994,120 (7): 2041~2061.
[104] Fathelbab F.A.,Tangent stiffness matrix for space frame members with both member and joint imperfections. Space Structures4.Thomas Telford, London, 1993,10(4):1323~1333.
[105] Dubina D.,Computation Models and Numerical Solution Procedures for Nonlinear of Single Layer Lattice Shells,International Joural of Space Structure, Vol.8,No.3,1993,PP321~333.
[106] GShi&S.N.Atluri,Elasto-plastic large Deformation Analysis of Space-Frames:A Plastic-Hinge and Stress-based Explicit Derivation of Tangent Stiffnesses, Internation Journal for Numerical methods in Engineering, Vo.26, 1988, PP589-615.
[107] J.H.Argyris,B.Borri,V.Hindenlang,M.Kleiber,Finite Element Analysis of Two-And Three-Dimensional Elasto-Plastic Frames—The Natural Approach, Comput. Meth.for Appl.Mech.Engng.,Vo.35,1982,PP221 -248.
[108] T See, R E Mcconnell. Large displacement elasic buckling of space structures. J. Struct. Engng,Vol.112,No.5,1986,PP1052-1069.
[109] E Riks. An incremental approach to the solution of snapping and buckling problems. Int.J.Solids Structures,Vo115,1979,pp529-551.
[110] M A Crisfield. An arc-length method including line searches and accelerations. Int.J. of Num. Mech.Eng.,Vo119,1983,pp1269-1289.
[111] R.D wood,O.C. Zienkiewicz,Geometrically nonlinear finite element analysis of beams,frames, arches and axisymmetric shells,Comp.and Struct,Vol.7,1977.
[112] Yang Y.B.,Kuo S.R.Theory& Analysis of nonlinear framed structures.Prentice Hall: 1994.170~234.
[113] Wang N.,Chen X., Shen S. Z. Geometric and material nonlinear analysis of latticed shells of negative Gaussoan curvature, Space Structures. Thomas Telford, London, 1993., 10 (4) : 649 ~ 654.
[114] Yamashita T., Kunieda H.Geometrical Nonlinear Analsis of Single -layer Latticed Dome. IASS, 1990 ,12(6):476~509.
[115] Choong K.K., Hangai Y.Review on methods of bifurcation analysis for geometrically nonlinear structure.Bulletin of the IASS, 1993, 34, 133-149.
[116] Clarke M.J.,Hancock Y.A study of increment-iterative strategies for nonlinear ananlyses.Journal of Numerical Methods in Engineering, 1990, 29: 1365~1391.
[117] Ramm.E.Strategies for Tracing the non-linear response near limit points.In:Wunderlich W,Stein E and Bathe KJ eds.Non-Linear Finite Elenent Analysis in Structural Mechanics,1981:63-89.
[118] Theodore V.Galambos,Robert L.Ketter.Columns under combined bending and thrust. Journal of Engineering Mechanics Division, 1959, 85(2): 1-30
[119] J.H.Argyris,An excursion into large rotations, Comp. Meth. Appl, Mech, Engng., 1982,32:85-155.
[120] R.B.Fuller,Non-symmetrical tension-integrity structures, U.S. Patent, Aug. 7,1973,No.3866366.
[121] Sleeb A.F.,Gendy A.S. Shear-flexible models for spatial bucking of thin-walled curved beams.Journal of Numerical Methods in Engineering. 1991,31(4): 729 ~ 759.
[122] Chen W.F.,Kim S .E.LEFD steel design using advanced analysis .CRC Press: 1997.
[123] J.L.Meek,H.S.Tan,Geometrically Non-Linear Analysis of Space Frames by An Incremental Iterative, Comput. Meth. forAppl. Mech. Engng., Vo.47, 1984, PP261-282.
[124] R.Srilard,Critical Load and Post-Buckling Analysis of Space Frames by Finite Element Method Using Energy Balancing Technique, Comput.Struct.,Vo. 20, No.l-3,1985,PP277-286.
[125] F.S. William, An approach to the nonlinear behaviour of the members of a rigid jointed plane framework with finite element deflections,.J. MechAppl. Math., Val.17,1964.
[126] R.K. Wen, Nonlinear elastic frame analysis by finite element,J Struct. Eng., Vol.109,1983.
[127] J.Jconnor.R.D.Logcher&S.C.Chan,Nonlinear analysis of elastic framed structures, J.Struct.Div, ASCE1968,94,1525~1547.
[128] B.A.Schrefler&S. A total lagrangian geometrically non-linear analysisof combined beam and cable structures,Comp & Struct, 1983 ,17:115-127.
[129] Zhang Qilin,Ineremental finite element solution for nonlinear problems of space truss,J.Construct.Steel Research, 19961,20:89-104.
[130] R.K.Wen &J.Rahimzadeh,Nonlinear finite elastic frame analysis by finite element,J.Struct.Engng.,ASCE,1983,109:1952-1971.
[131] K.J.Bathe & S.Bolourchi,Large displacement analysis of three- dimensional beam structures,Int.J.Num.Meth.Engng., 1979,14:961 -989.
[132] E.Riks,The application of Newton's method to the problem of elastic stability,J. Appl.Mech.,1972,39:1060-1066.
[133] M.A.Crisfield,A fast incremental/iterative solution procedure that handles "snap-through",Comp.& Struct., 1981,13:55-62.
[134] M.A.Crisfied,An arc-length method including line searehes and accelerations,Int.J.Num.Meth.Engng., 1983,19:1269-1289.
[135] M.A.Clarke &GJ.hancock,A study of incremental-iterative strategies for non-linear analysis, Int. J. Num. Meth, Engng, 1990,29 : 1365 -1391.
[136] Lind N.C.Local instability analysis of triangulated dome frameworks. The Structure Engeneer, 1969,47(8) :317 ~ 324.
[137] White D.W.Plastic-hinge methods for advanced analysis of steel frames. Journal of the Construction Steel Research,1993,24:121~152.
[138] White D.W.,Richard J.Y.,Chen W.F.Second-order inelastic analysis for frame design:A report to SSRC task group 29 on recent research and the perceived state-of-the-Art,Structural Engineering CE- STR- 91- 12, School of Civil Engineering,Purdue University, 1991.
[139] King W.S., White D.W., Chen W.F.Second order inelastic analysis methods for steel-frame design. Journal of Structural Engineering, 1992,118(2): 408-428.
[140] Orbison J.G, McGuire W.,Abel J.F.Yield surface applications in nonlinear steel frame analysis.Computer Methods in Applied Mechanics and Engineering, 1982,33:557-573.
[141] Ziemian R.D., McGuire W., Deierlien G.Inelestic limit states design.Part II: Three-dimensionla frame studies. Journal of the Structural Engineering, 1992, 118(9):2550-2568
[142] Richard J.Y., Whete D.W., Chen W.F.Second-order refined plastic-hinge analysis for frame design.Part I.Journal of Structural Engineering, 1993, 119(11): 3196-3216.
[143] White D.W.Material and Geometric Nonlinear analysis of local planar behavior in steel frames using interactive computer graphics:MS Thesis,Cornell Univ., Ithaca,N.Y1985.
[144] Chen W.F,Atsuta T.Theory of beam-columns.Volume 1:In-plane behavior and design.New York:McGraw-Hill,1976.
[145] Chen W.F,Atsuta T.Theory of beam-columns.Volume 2:Space behavior and design.New York:McGraw-Hill,1976.
[146] Al-Mashary F., Chen W.F. Simplified second-order inelastic analysis for steel frames.The Structural Engineer, 1991,69(23):395-399.
[147] King W.S.A Modified stiffness method for plastic analysis of steel frames.Engineering Structures, 1994,16(3): 162-170.
[148] Richard J.Y., White D.W,Chen W.F.Notional-load plastic-hinge method for frame design, Journal of Structural Engineering, 1994,120 (5): 1434-1454.
[149] Duan L., Chen W.F.Design interaction equation for steel beam-columns.Journal of Structural Engineering, 1989,115(5): 1225-1243. 150 、 Zhou S.P.,Duan L.,Chen W.F. Comparison of design equations for steel beam-columns. Structural Engineering Review, 1990,2(1):45-53