A Deformation Field for Euler-Bernoulli Beams with Applications to Flexible Multibody Dynamics

The deformation eld commonly used for Euler-Bernoulli beams in structural dynamics is investigated to determine its suitability for use in exible multibody dynamics. It is found that the traditional deformation eld fails to produce an elastic rotation matrix that is complete to second order in the deformation variables. A complete second-order deformation eld is proposed along with the equations needed to incorporate the beam model into a graph-theoretic formulation for exible 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 polyno-mials as the basis functions in a Rayleigh-Ritz discretization of the beam's deformation variables. To demonstrate the eeects of the proposed second-order deformation eld on the response of a exible multibody system, two examples are presented.