Formulation of a geometrically nonlinear 3D beam finite element based on kinematic-group approach

A relatively simple finite element with 12 degrees of freedom is proposed for geometrically nonlinear analysis of spatial shear deformable beams and rods. The finite-element formulation is based on the concept of kinematic group, which is a geometrical object comprising two nodes on the rod axis and two adjoined vectors (directors) which define orientation of the cross section at each node. Results of sample problems are given to show the applicability of the element to study nonlinear deformation and stability of three-dimensional elastic rods undergoing finite rotations.