An efficient 3D corotational beam formulation using hybrid spatial discretization for nonlinear dynamics of flexible multibody system

Abstract

In this paper, an efficient and accurate 3D corotational beam formulation in fully explicit form is proposed for the nonlinear dynamics of flexible multibody systems. A hybrid spatial discretization scheme is presented, in which the internal force terms are described in the local frame and the inertial force terms are described in the global frame. The local frame is used to decompose rigid motions and deformations, which ensures the objectivity of the rotational interpolation for the internal force evaluation. The nonlinear internal terms can be explicitly derived in the local frame based on the second-order approximation of the three-dimensional finite-elasticity theory. For inertial terms, velocity and acceleration can be obtained in simple and concise forms by utilizing the global discretization scheme. Combined with the precise orientation approximation provided by the corotational frame, the inertial terms can also be derived explicitly. Therefore, Gaussian quadrature is no longer required in the presented formulation. Finally, some classic examples are employed to verify the accuracy and efficiency compared to two widely used corotational beam formulations. The results indicate that the presented formulation not only matches the accuracy of the conventional cubic formulation but also provides a clear advantage in computational efficiency due to the fully explicit form.