NDLI: A quaternion-based formulation of Euler–Bernoulli beam without singularity

Content Provider	Springer Nature Link
Author	Zhao, Zhihua Ren, Gexue
Copyright Year	2011
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.
Starting Page	1825
Ending Page	1835
Page Count	11
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	67
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-06-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Euler–Bernoulli beam Quaternion Finite element Large deformation Torsion Gyroscopic effect Automotive Engineering Vibration, Dynamical Systems, Control Mechanical Engineering Mechanics
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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