5/6 DOFS CB SHELL ELEMENTS BASED ON THE LOCAL FRAME OF SE(3) GROUP

The modeling method based on the local frame of Lie group (LFLG) for flexible multibody dynamics can naturally eliminate the geometric nonlinearity of the overall rigid motion, so that the generalized internal forces and inertial forces as well as their Jacobian matrices are invariant under the arbitrary rigid body motion. In this paper, a novel 5 Dofs continuum-based (CB) shell element based on the LFLG is proposed by integrating the idea of the LFLG and the CB shell theory. Compared with the geometrically exact shell element based on the LFLG, the proposed shell element greatly simplifies the complexity caused by the interpolation, and the discretized strain tensors naturally satisfy the objectivity. At the same time, the finite element discretization and variational operations are commutative, which further simplifies the computation of the generalized internal forces and their Jacobian matrices. To deal with the composite structure conveniently, the relationship between the mid-surface motion and the drilling Dofs is established by the polar decomposition of the mid-surface deformation gradient tensor on the basis of the 5 Dofs CB shell element. Then, a 6 Dofs CB shell element based on the LFLG is proposed. To improve the convergence accuracy of the proposed elements, the two-field Hellinger-Reissner variational principle and the assumed natural strain (ANS) method are used to alleviate the in-plane and transverse shear locking, respectively. Several static examples are presented to verify the convergence accuracy of the 6 Dofs CB shell element. A dynamic example is presented to demonstrate that the 6 Dofs CB shell element can eliminate the geometric nonlinearity of the overall rigid motion.