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.