Co-rotational 3D beam element using quaternion algebra to account for large rotations: Dynamic equilibrium and applications

This paper presents a new co-rotational beam element based on quaternion algebra as parametrization of large rotations for dynamic applications. The co-rotational framework is based on a decomposition of the kinematics into a rigid element frame (that follows the element) and its pure deformation. Based on a previous work related to the static equilibrium, the proposed co-rotational element lies in the framework of the incremental formulations. The kinematic field description using quaternion algebra allows to calculate quaternion’s velocities and accelerations. Then, the dynamic equilibrium and the formulation of the internal mass matrix and gyroscopic terms are detailed. Seven numerical applications in dynamic conditions are presented and compared with literature results showing the response of the proposed element in terms of conservation of the energy and convergence. •Quaternion parametrization of large rotations in a dynamic co-rotational framework.•Dynamic operators are obtained using quaternion’s velocities and accelerations.•Linearization of the response to obtain a dynamic algorithmic tangent operator.•Seven distinct dynamic study cases are presented showing numerical capabilities.