Analysis of flexible multibody systems with spatial beams using mixed variational principles

B. M. Quadrelli, S. N. Atluri

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A general finite element formulation is presented for dynamic analysis of spatial elastic beams, for small strains, in a multi-body configuration. The tangent maps associated to the finite rotation vector are used to compute the tangent matrices used to integrate implicitly the equations of motion in descriptor form. A corotational method and a mixed variational method are used to compute the tangent stiffness matrix. The tangent constraint matrices are obtained using consistent linearization of the constraint equations. The tangent inertia matrices, including the gyroscopic and centrifugal terms, are also obtained by using the tangent maps of rotation. The numerical examples analyzed in this paper include: dynamic analysis of flexible beam structures and multi-flexible body systems with open and closed kinematic loops. A comparison with the previous results in the literature shows a very good performance in terms of time integration step and number of elements used.

Original languageEnglish
Pages (from-to)1071-1090
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Jul 30 1998


  • Beam finite elements
  • Finite rotation
  • Flexible multibody dynamics
  • Variational principles


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