Nonlinear Beam Element with Meshed Sections
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摘要: 为准确描述材料进入非线性阶段后的应力状态,针对采用梁单元时框架结构材料非线性的有限元分析问题,提出了基于分布式塑性理论的三维材料非线性梁单元分析方法——网格截面梁单元法,并通过算例对其有效性和准确性进行了验证.这种方法采用平面等参单元将梁单元截面网格化,通过引入材料本构模型,由截面网格材料的应力-应变关系和应力分别积分得到梁单元的截面刚度矩阵和截面抗力,再通过位移插值函数计算梁单元在材料进入非线性阶段时的单元刚度矩阵和节点抗力.Abstract: Based on the distributed plasticity approach,a new kind of beam element,3-D materially nonlinear beam element with meshed sections,was presented to analyze the materially nonlinear behaviour of frame structures accurately,and a numerical example for the elasto-plastic analysis of a cantilever beam was given to illustrate the accuracy and efficiency of this approach.With this approach,beam sections are discretized into planar isoparametric elements at the integral points along the longitudinal direction of beam element,the stiffness matrices and resistant forces of sections are calculated by introducing the nonlinear stress-strain relations of materials and respectively integrating the stress-strain relations and stresses of sections,and the element stiffness and nodal resistant forces can also be evaluated with displacement interpolation functions when materials are in a nonlinear state.
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BATHE K J.Finite element procedure in engineering analysis[M].Englewood Cliffs,New Jersey:Prentice-Hall,Inc.,1982:485-557.[2] CRISFIELD M A.Non-linear finite element analysis of solids and structures:Volume 1[M].New York:John Wiley Sons,1991:152-197.[3] CHAN E C.Nonlinear geometric,material and time dependent analysis of reinforced concrete shells with edge beams[D].Berkeley:Department of Civil Engineering,University of California,1982.[4] MARI A R.Nonlinear geometric,material and time-dependent analysis of three dimensional reinforced concrete frames[D].Berkeley:Department of Civil Engineering,University of California,1984.[5] IZZUDDIN B A,ELNASHAI A S.Adaptive space frame analysis-Part II:A distributed plasticity approach[J].Structures and Buildings Journal,1993,99(3):317-326.[6] SPACONE E,FILIPPOU F C,TAUCER F F.Fiber beam-column model for non-linear analysis of R/C frames (part I):Formulation[J].Earthquake Engineering and Structural Dynamics,1996,25(7):711-725.[7] SPACONE E,FILIPPOU F C,TAUCER F F.Fiber beam-column model for non-linear analysis of R/C frames (part II):Applications[J].Earthquake Engineering and Structural Dynamics,1996,25(7):727-742.[8] 周凌远.斜拉桥非线性理论及极限承载力研究[D].成都:西南交通大学土木工程学院,2007.[9] 朱伯芳.有限单元法原理与应用[M].2版.北京:中国水利水电出版社,1998:112-127.[10] LAM W F,MORLEY C T.Arc-length method for passing limit points in structural calculation[J].Journal of Structural Engineering,1992,118(1):169-185.
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