A quaternion-based formulation of Euler–Bernoulli beam without singularity |
| |
Authors: | Zhihua Zhao Gexue Ren |
| |
Institution: | 1.School of Aerospace,Tsinghua University,Beijing,China |
| |
Abstract: | This paper proposes a singularity-free beam element with Euler–Bernoulli assumption, i.e., the cross section remains rigid
and perpendicular to the tangent of the centerline during deformation. Each node of this two-nodal beam element has eight
nodal coordinates, including three global positions and one normal strain to describe the rigid translation and flexible deformation
of the centerline, respectively, four Euler parameters or quaternion to represent the attitude of cross section. Adopting
quaternion instead of Eulerian angles as nodal variables avoids the traditionally encountered singularity problem. The rigid
cross section assumption is automatically satisfied. To guarantee the perpendicularity of cross section to the deformed neutral
axes, the position and orientation coordinates are coupled interpolated by a special method developed here. The proposed beam
element allows arbitrary spatial rigid motion, and large bending, extension, and torsion deformation. The resulting governing
equations include normalization constraint equations for each quaternion of the beam nodes, and can be directly solved by
the available differential algebraic equation (DAE) solvers. Finally, several numerical examples are presented to verify the
large deformation, natural frequencies and dynamic behavior of the proposed beam element. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|