考虑剪切效应三维纤维梁单元的几何非线性增量有限元分析

该文以三维连续介质力学和虚功原理为基础,推导了增量U.L.有限元列式,该列式保留了大位移刚度矩阵项,并对该刚度矩阵进行修正使其成为对称矩阵。根据增量U.L.列式,推导了三维纤维梁单元的刚度矩阵。该单元采用平截面假定,以轴向节点位移表示截面上任意一点的位移,并结合Timoshenko梁理论来考虑剪切效应。以上原理编制分析程序,通过几个算例分析,证明了该方法的精确性、通用性。

GEOMETRICALLY NONLINEAR INCREMENTAL FINITE ELEMENT ANALYSIS OF 3D FIBER BEAM ELEMENT CONSIDERING SHEAR EFFECT

Based on continuum mechanics and the principle of virtual displacements, incremental updated Lagrangian formulation (U.L.) was presented. A large displacement stiffness matrix was considered in U.L., which was rectified to be a symmetrical matrix. According to U.L., a three-dimensional fiber-beam-element tangent-stiffness matrix was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in view of nodal displacements, and the shear effect was taken account in combination with Timoshenko beam theory. Furthermore, the nonlinear finite element method program has been developed and a series of numerical examples were given to demonstrate the behavior, the accuracy and generality of the three-dimensional fiber-beam element.