Nonlinear static and dynamic analysis of corotational shell formulated on the special Euclidean group SE(3)

This paper presents a new framework for corotational shell elements. The traditional corotational formulation uses local element frames, which greatly facilitates the calculation of elastic forces. However, all force vectors eventually need to be transformed into the global frame, resulting in the loss of invariance. The special Euclidean group SE(3) is introduced to describe the kinematics of the corotational shell element in the local frame. The equations of motion are established, in which the internal forces, inertial forces and tangent matrices are systematically derived in the SE(3) framework. The force vectors and their derivative matrices under the SE(3) description eliminate the effect of the rigid body motion, which is only related to the local deformation of the elements. Some examples are used to verify the validity and efficiency of the presented corotational shell element based on SE(3) to handle geometrically nonlinear problems. The results demonstrate that the SE(3) framework has higher computational efficiency with larger step size compared to the Lie group R³ × SO(3). According to the framework invariance brought by SE(3), a constant mass matrix during iterations is adopted to deal with the nonlinear problems with large rotation and small strain, which can significantly reduce the computational time. In summary, the results of the study show that the SE(3) framework has better characteristics and broader application prospects.