三维纤维梁单元增量非线性有限元分析

Incremental Nonlinear Finite Element Analysis of 3D Fiber Beam Element

摘要:

本文以三维连续体介质力学和虚位移原理为基础，推导了增量U.L.列式，此列式中保留了大位移刚度矩阵项，并对此刚度矩阵进行修正使其成为对称矩阵。根据增量U.L.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。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。

Abstract:

Based on continuum mechanics and the principle of virtual displacements, incremental updated Lagrangian formulation (U.L.) were presented. The large displacement stiffness matrix was considered in U.L., 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 has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional fiber beam element.