A higher order formulation for geometrically nonlinear space beam element

This paper derives a refined finite element for geometrically nonlinear analysis of space frames in updated Lagrangian framework. A new incremental tangent stiffness matrix, which allows for high order effects of element deformation, replaces the conventional incremental scant stiffness matrix. Two deformation matrices due to axial force and moment are derived. They are the functions of element deformations and incorporated with the coupling among axial, lateral and torsional deformations. The proposed matrices are used together with the linear and geometric stiffness for beam elements to analyze the deflection behavior of space frames. Numerical examples demonstrate that the proposed element is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and lateral-torsional, of space frames even when less elements are used to model a new member.