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The quaternion-based three-dimensional beam theory

✍ Scribed by E. Zupan; M. Saje; D. Zupan

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
587 KB
Volume
198
Category
Article
ISSN
0045-7825

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✦ Synopsis

This paper presents the equations for the implementation of rotational quaternions in the geometrically exact three-dimensional beam theory. A new finite-element formulation is proposed in which the rotational quaternions are used for parametrization of rotations along the length of the beam. The formulation also satisfies the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal in its weak form. A strict use of the quaternion algebra in the derivation of governing equations and for the numerical solution is presented. Several numerical examples demonstrate the validity, performance and accuracy of the proposed approach.

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