三维纤维梁单元增量非线性有限元分析
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摘要
以三维连续体介质力学和虚位移原理为基础,推导了增量更新拉格朗日(UL)列式,此列式中保留了大位移增量刚度矩阵项,并对此刚度矩阵进行修正使其成为对称矩阵.根据增量UL列式,推导出小应变、大位移、大转动三维纤维梁刚度矩阵.该梁单元的刚度矩阵考虑了复合材料非线性、大位移、大转动高度几何非线性.该单元采用平截面假定,忽略剪切变形的影响,以轴线节点的位移表示截面上任意一点位移.根据以上理论编制了分析程序,通过对几个算例分析,证明该方法的精确性、通用性.
Based on continuum mechanics and the principle of virtual displacements,the incremental updated Lagrangian formulation(UL) was presented.The large displacement stiffness matrix was considered in UL,which was rectified to be symmetrical matrix.According to the incremental updated Lagrangian formulation,small strain,large displacement,finite rotation of three dimensional fiber beam element tangent stiffness matrix was developed.Considering the nonlinear constitutive relationship of composites,large displacement and finite rotation,a new type of tangent stiffness matrix of the beam element was presented.According to the basic assumption of plane section,the displacement field of an arbitrary fiber was presented in terms of nodal displacement,and shear deformation effect was not taken account.Furthermore,a nonlinear finite element method program was developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional fiber beam element.
Based on continuum mechanics and the principle of virtual displacements,the incremental updated Lagrangian formulation(UL) was presented.The large displacement stiffness matrix was considered in UL,which was rectified to be symmetrical matrix.According to the incremental updated Lagrangian formulation,small strain,large displacement,finite rotation of three dimensional fiber beam element tangent stiffness matrix was developed.Considering the nonlinear constitutive relationship of composites,large displacement and finite rotation,a new type of tangent stiffness matrix of the beam element was presented.According to the basic assumption of plane section,the displacement field of an arbitrary fiber was presented in terms of nodal displacement,and shear deformation effect was not taken account.Furthermore,a nonlinear finite element method program was developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional fiber beam element.
引文
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[13]Menegotto M,Pinto P E,Method of analysis for cyclicallyloaded reinforced concrete Plane frames including changes ingeometry and non-elastic behavior of elements under combinednormal force and bending[C]//Proceedings,IABSESymposium on Resistance and Ultimate Deformability ofStructures Acted on by Well-Defined Repeated Loads.Lisbon:IABSE,1973:15-20.
[14]YANG Yeongbin.Theory and analysis of nonlinear framedstructures[M].[S.l.]:Prentice-Hall,Inc,1994.
[15]禚一,李忠献.基于显式算法的纤维梁柱单元模型[J].工程力学,2011,28(12):39.ZHUO Yi,LI Zhongxian.Explicit algorithm-based fiber beamcolumn element model[J].Engineering Mechanics,2011,28(12):39.
[16]William F W.An approach to the non-linear behaviour of themembers of a rigid jointed plane framework with finitedeflections[J].The Quarterly Journal of Mechanics&AppliedMathematics,1964,17(4):451.
[17]Shi G,Atluri S N.Elasto-plastic large deformation analysis ofspace-frames:a plastic-hinge and stress-based explicitderivation of tangent stiffnesses[J].International Journal forNumerical Methods in Engineering,1988,26(3):589.
[18]Park M S,Lee B C.Geometrically non-linear and elastoplasticthree dimensional shear flexible beam element of von-mises-type hardending material[J].International Journal forNumerical Methods in Engineering,1996,99(3):383.
[2]Spacone E,Filippou F C,Taucer F F.Fiber beam-columnmodel for nonlinear analysis of R/C frames:part I.Formulation[J].Earthquake Engineering and StructuralDynamics,1996,25:711.
[3]陈滔,黄宗明.基于有限单元柔度法的材料与几何双重非线性空间梁柱单元[J].计算力学学报,2006,23(5):524.CHEN Tao,HUANG Zongming.Material and geometricallynonlinear spatial beam-column element based on the finiteelement flexibility method[J].Chinese Journal ofComputational Mechanics,2006,23(5):524.
[4]聂建国,陶慕轩.采用纤维梁单元分析钢-混凝土组合结构地震反应的原理[J].建筑结构学报,2011,32(10):1.NIE Jianguo,TAO Muxuan.Theory of seismic responseanalysis of steel-concrete composite structures using fiber beamelements[J].Journal of Building Structures,2011,32(10):1.
[5]李易,陆新征,叶列平,等.混凝土框架结构火灾连续倒塌数值分析模型[J].工程力学,2012,29(4):96.LI Yi,LU Xinzheng,YE Lieping,et al.Numerical models offire induced progressive collapse analysis for reinforcedconcrete frame structures[J].Engineering Mechanics,2012,29(4):96.
[6]Zubydan A H,ElSabbagh A I.Monotonic and cyclic behavior ofconcrete-filled steel-tube beam-columns considering localbuckling effect[J].Thin-Walled Structures,2011,49(4):465.
[7]Thai H T,Kim S E.Second-order inelastic analysis of cable-stayed bridges[J].Finite Elements in Analysis and Design,2012,53:48.
[8]Zupan D,Saje M.The linearized three-dimensional beamtheory of naturally curved and twisted beams:the strainvectors formulation[J].Computer Methods in AppliedMechanics and Engineering,2006,195(33/36):4557.
[9]Bathe K J,Wilson E L.Nonsap—a nonlinear structuralanalysis program[J].Nuclear Engineering and Design,1974,29:266.
[10]Riks E.An incremental approach to the solution of snappingand buckling problems[J].International Journal of Solids andStructures,1979,15(7):529.
[11]Crisfield M A.An arc-length method including line searches andaccelerations[J].International Journal for Numerical Methodsin Engineering,1983,19(9):1269.
[12]Taucer F F,Spacone E,Filippou F C.A fiber beam-columnelement for seismic response analysis of reinforced concretestructures[R].Berkeley:Earthquake Engineering ResearchCenter of University of California,Berkeley,1991.
[13]Menegotto M,Pinto P E,Method of analysis for cyclicallyloaded reinforced concrete Plane frames including changes ingeometry and non-elastic behavior of elements under combinednormal force and bending[C]//Proceedings,IABSESymposium on Resistance and Ultimate Deformability ofStructures Acted on by Well-Defined Repeated Loads.Lisbon:IABSE,1973:15-20.
[14]YANG Yeongbin.Theory and analysis of nonlinear framedstructures[M].[S.l.]:Prentice-Hall,Inc,1994.
[15]禚一,李忠献.基于显式算法的纤维梁柱单元模型[J].工程力学,2011,28(12):39.ZHUO Yi,LI Zhongxian.Explicit algorithm-based fiber beamcolumn element model[J].Engineering Mechanics,2011,28(12):39.
[16]William F W.An approach to the non-linear behaviour of themembers of a rigid jointed plane framework with finitedeflections[J].The Quarterly Journal of Mechanics&AppliedMathematics,1964,17(4):451.
[17]Shi G,Atluri S N.Elasto-plastic large deformation analysis ofspace-frames:a plastic-hinge and stress-based explicitderivation of tangent stiffnesses[J].International Journal forNumerical Methods in Engineering,1988,26(3):589.
[18]Park M S,Lee B C.Geometrically non-linear and elastoplasticthree dimensional shear flexible beam element of von-mises-type hardending material[J].International Journal forNumerical Methods in Engineering,1996,99(3):383.
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