The quaternion-based three-dimensional beam theory

Eva Zupan in Miran Saje in Dejan Zupan (2009) The quaternion-based three-dimensional beam theory. Computer Methods in Applied Mechanics and Engineering, 198 (49-52). str. 3944-3956. ISSN 0045-7825

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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. (C) 2009 Elsevier B.V. All rights reserved.

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