A total Lagrangian, objective and intrinsically locking‐free Petrov–Galerkin <i>SE</i> (3) Cosserat rod finite element formulation

Based on more than three decades of rod finite element theory, this publication unifies all the successful contributions found in literature and eradicates arising drawbacks like loss objectivity, locking, path-dependence redundant coordinates. Specifically, idea interpolating nodal orientations using relative rotation vectors, proposed by Crisfield Jeleni\'c 1999, is extended to interpolation Euclidean transformation matrices with aid twists; a strategy that arises from SE(3)-structure Cosserat kinematics. Applying Petrov-Galerkin projection method, we propose novel formulation where virtual displacements rotations as well translational angular velocities are interpolated instead consistent variations time-derivatives introduced formula. Properties such intrinsic absence preservation objectivity after discretization parametrization terms minimal number unknowns demonstrated conclusive numerical examples both statics dynamics.