钢管混凝土结构材料非线性的一种有限元分析方法
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摘要
为了更简单地考虑梁单元的材料非线性受力性能,把断面广义力和广义应变的概念运用于单元分析中,将单元的弹塑性刚度矩阵分离为弹性刚度矩阵和塑性刚度矩阵。这样,梁单元的变形可以由弹性变形和塑性变形简单地迭加,结构内力可通过弹性应变能的斜率(弹性刚度矩阵)与位移的乘积求得,从而在增量-迭代计算时可较准确且较快地计算出结构变形后的不平衡力。应用这一计算方法,推导了基于纤维模型的三维梁单元的钢管混凝土结构的有限元基本公式,并将其植入能考虑几何非线性的三维梁单元非线性计算程序NL_Beam3D中以计算结构的双重非线性问题。算例分析表明该方法和程序能较准确地反映钢管混凝土结构的双重非线性特性。
Applying generalized force and strain into element analysis, the elastic-plastic stiffness matrix is readily separated into elastic and plastic stiffness matrices in which the material nonlinearity of a beam element are taken into account. The total deformation of the beam element can be accordingly obtained by imposing plastic deformation on elastic deformation, and the internal force can be obtained by multiplying the slope of elastic strain energy (elastic stiffness matrix) with the deformation, so the unbalanced forces after deformation can be calculated more quickly and accurately during iterative analysis. Based on the above-mentioned procedure and so called fiber-model beam element, the primary finite element formula is derived for concrete filled steel tubular structures. This formula is implemented in a geometrically nonlinear finite element analysis computer program NL_Beam3D based on the 3-D beam element, to solve dual-nonlinearity problem. The proposed method and procedure are verified in a case to describe nonlinear behaviors of the concrete filled steel tubular structure accurately.
Applying generalized force and strain into element analysis, the elastic-plastic stiffness matrix is readily separated into elastic and plastic stiffness matrices in which the material nonlinearity of a beam element are taken into account. The total deformation of the beam element can be accordingly obtained by imposing plastic deformation on elastic deformation, and the internal force can be obtained by multiplying the slope of elastic strain energy (elastic stiffness matrix) with the deformation, so the unbalanced forces after deformation can be calculated more quickly and accurately during iterative analysis. Based on the above-mentioned procedure and so called fiber-model beam element, the primary finite element formula is derived for concrete filled steel tubular structures. This formula is implemented in a geometrically nonlinear finite element analysis computer program NL_Beam3D based on the 3-D beam element, to solve dual-nonlinearity problem. The proposed method and procedure are verified in a case to describe nonlinear behaviors of the concrete filled steel tubular structure accurately.
引文
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[15]Chen W F,Atsuta T.Theory of beam-columns,Vol.2:Space behaviors and design[M].USA:McGraw-Hill International Book Company,1977.
[16]Ziegler H.A modification of prager’s hardening rule[J].Quarterly of Applied Mathematics,1959,17(1):55―65.
[17]Ristic D,Yamada Y,Iemura H.Stress-strain based modeling of hysteretic structures under earthquake induced bending and varying axial loads[D].Japan:School of Civil Engineering,Kyoto University,1986.
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[19]陈宝春,陈友杰.钢管混凝土肋拱面内受力全过程试验研究[J].工程力学,2000,17(2):44―50.Chen Baochun,Chen Youjie.Experimental study on mechanic behaviors of concrete-filled steel tubular rib arch under in-plane loads[J].Engineering Mechanics,2000,17(2):44―50.(in Chinese)
[2]陈宝春.钢管混凝土拱桥(第2版)[M].北京:人民交通出版社,2007.Chen Baochun.Concrete filled steel tubular arch bridges(2nd Edition)[M].Beijing:China Communications Press,2007.(in Chinese)
[3]钟善桐.钢管混凝土结构(第3版)[M].北京:清华大学出版社,2003.Zhong Shantong.The concrete-filled steel tubular structures(3rd Edition)[M].Beijing:Tsinghua University Press,2003.(in Chinese)
[4]蔡绍怀.现代钢管混凝土结构[M].北京:人民交通出版社,2003.Cai Shaohuai.Modern steel tube confined concrete structures[M].Beijing:China Communications Press,2003.(in Chinese)
[5]韩林海.钢管混凝土结构-理论与实践[M].北京:科学出版社,2004.Han Linhai.Concrete-filled steel tubular structure-theory and practice[M].Beijing:Science Press,2004.(in Chinese)
[6]胡世德,苏虹,王君杰.钢管混凝土拱桥的三维弹塑性地震反应理论分析[J].中国公路学报,2004,17(1):57―61.Hu Shide,Su Hong,Wang Junjie.3D elastic-plastic seismic response analysis for CFST bridge[J].China Journal of Highway and Transport,2004,17(1):57―61.(in Chinese)
[7]陈友杰,陈宝春.钢管混凝土单圆管肋拱非线性有限元分析[J].湘潭师范学院学报(自然科学版),2003,25(4):91―94.Chen Youjie,Chen Baochun.Nonlinear finite element analysis of concrete-filled steel tubular(single tube)rib arch[J].Journal of Xiangtan Normal University(Natural Science Edition),2003,25(4):91―94.(in Chinese)
[8]曾国锋,范立础,章关永.应用复合梁单元实现钢管混凝土拱桥的极限承载力分析[J].铁道学报,2003,25(5):97―102.Zeng Guofeng,Fan Lichu,Zhang Guanyong.Load capacity analysis of concrete filled steel tube arch bridge with the composite beam element[J].Journal of the China Railway Society,2003,25(5):97―102.(in Chinese)
[9]Morris G A,Fenves S J.Elastic-plastic analysis of frameworks[J].Journal of the Structural Division,1970,96(5):931―946.
[10]Attalla M R,Deierlein G G,McGuire W.Spread of plasticity:Quasi-plastic-hinge approach[J].Journal of the Structural Division,1994,120(8):2451―2473.
[11]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.Tong Genshu.In-plane stability of steel structures[M].Beijing:China Architecture&Building Press,2005.(in Chinese)
[12]谢旭.桥梁结构地震响应分析与抗震设计[M].北京:人民交通出版社,2006.Xie Xu.Seismic response and earthquake resistant design of bridges[M].Beijing:China Communications Press,2006.(in Chinese)
[13]Yamato Engineering Inc.Manual of Y-Fiber3D[M].Japan:Yamato Engineering Inc,2002.
[14]吴庆雄,陈宝春,韦建刚.三维杆系结构的几何非线性有限元分析[J].工程力学,2007,24(12):19―24.Wu Qingxiong,Chen Baochun,Wei Jiangang.A geometric nonlinear finite element analysis for3D framed structures[J].Engineering Mechanics,2007,24(12):19―24.(in Chinese)
[15]Chen W F,Atsuta T.Theory of beam-columns,Vol.2:Space behaviors and design[M].USA:McGraw-Hill International Book Company,1977.
[16]Ziegler H.A modification of prager’s hardening rule[J].Quarterly of Applied Mathematics,1959,17(1):55―65.
[17]Ristic D,Yamada Y,Iemura H.Stress-strain based modeling of hysteretic structures under earthquake induced bending and varying axial loads[D].Japan:School of Civil Engineering,Kyoto University,1986.
[18]Yang Y B,Shieh M S.Solution method for nonlinear problems with multiple critical points[J].AIAA Journal,1990,28(12):2110―2116.
[19]陈宝春,陈友杰.钢管混凝土肋拱面内受力全过程试验研究[J].工程力学,2000,17(2):44―50.Chen Baochun,Chen Youjie.Experimental study on mechanic behaviors of concrete-filled steel tubular rib arch under in-plane loads[J].Engineering Mechanics,2000,17(2):44―50.(in Chinese)
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