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

摘要

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 fails to produce an elastic rotation matrix that is complete to secondorder in the deformation variables. A complete second-order deformation field is proposed 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 deformation variables. To demonstrate the effects of the proposed second-order deformation field on the response of a flexible multibody system, two examples are presented.