Incremental Nonlinear Finite Element Analysis of 3D Fiber Beam Element

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.