A 3D corotational beam element formulated on the special Euclidean group SE(3)

Abstract

A 3D corotational beam element reformulated under the framework of special Euclidean group is proposed in this paper. The corotational method can largely facilitate the evaluation of internal elastic forces by introducing a local element frame. However, all the force vectors are finally expressed in the global frame which leads to the loss of invariance. In this work, the special Euclidean group SE(3) is introduced to describe the rigid body motion. The equations of motion are expressed in the local nodal frames. The force vectors and their corresponding tangent matrix are invariant under superimposed rigid body motions which can reduce the nonlinearity of the equations. The reformulation of the element matrices is performed by direct coordinate transformation. The advantage of this transformation is demonstrated by numerical examples. It shows that the SE(3) description of motion can decrease the iteration numbers under a large time step or load step. The iteration matrix for the SE(3) description, can be kept invariant for structures undergoing large displacements and large rotations while the deformation of which is small. The results of this work show that the SE(3) framework displays more advantages and prospects in terms of computational efficiency compared with the original R3×SO(3) framework.