On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra

International audienceIn the paper, we present the Reissner–Simo beam theory in which the rotations are represented by quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered and the consistent energy complements of the rotational quaternions are employed, we derive the weak kinematic equations in the quaternion-based description. These equations are then employed in the extended virtual work principle to obtain the consistent governing equations of the three-dimensional beam in terms of the quaternion algebra. The quaternion moment equilibrium equation is analyzed, discussed, and interpreted. In numerical implementation, the standard Galerkin discretization is used to obtain the quaternion-based finite-element formulation. Various examples prove the suitability of the formulation