A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematic description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant–Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad's formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique.