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    三维退化纤维梁单元线性和非线性有限元分析
    康澜, 张其林
    同济大学 土木工程学院建筑工程系,上海 200092
    摘要:
    为了解决曲线梁、任意形状截面梁、以及复合材料梁等结构的计算问题,基于退化理论推导得到三维退化纤维梁单元。该单元采用平截面基本假设,考虑剪切变形的影响,用轴线节点位移表示梁单元任意一点的三维位移场。根据UL列式,推导得到该单元考虑几何非线性和材料非线性的切线刚度矩阵。由上述理论编制了有限元计算程序,通过对几个典型算例的分析,证明了这种纤维退化梁单元的精确性、高效性和通用性。
    关键词:  三维退化纤维梁单元  复合材料梁  任意形状截面  非线性有限元
    DOI:10.11835/j.issn.1674-4764.2009.02.002
    分类号:
    基金项目:世博轴超大跨度索膜及单层复杂壳体结构专项技术研究(08dz0580303)
    Linear and Nonlinear Finite Element Analysis of a Degenerated 3D Beam Element
    KANG Lan, ZHANG Qilin
    Department of Building Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, P. R. China
    Abstract:
    In order to solve the calculation problems of the curved beam, an arbitrary cross section beam and composite beam, a degenerated 3D fiber beam element is derived based on the degenerated theory. According to the basic assumption of plane section, the 3D displacement field equations of an arbitrary point are discretized in terms of nodal displacements, which take account of shear deformation effect. Furthermore, the tangent stiffness matrix formulation, which takes geometric and material nonlinearity into account, is deduced using Update Lagrange formulation. A finite element method program has been developed, and several typical examples are tested to demonstrate the effectiveness, accuracy and versatility of this beam element.
    Key words:  3D degenerated fiber beam element  composite beam  arbitrary cross section  nonlinear finite element
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