A deformation field for Euler-Bernoulli beams with applications to flexible multibody dynamics

The deformation field commonly used for Euler-Bernoulli beams in structural dynamics is investigated to determine its suitability for use in flexible multibody dynamics. It is found that the traditional deformation field fail s to produce an elastic rotation matrix that is complete to second-order in the deformation variables. A complete second-order deformation field is pr oposed along with the equations needed to incorporate the beam model into a graph-theoretic formulation for flexible multibody dynamics [1]. This beam model and formulation have been implemented in a symbolic computer program called DynaFlex that can use Taylor, Chebyshev, or Legendre polynomials as the basis functions in a Rayleigh-Ritz discretization of the beam's deform ation variables. To demonstrate the effects of the proposed second-order de formation field on the response of a flexible multibody system, two example s are presented.