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

The deformation field commonly used for Euler–Bernoulli beamsin structural dynamics is investigated to determine its suitability foruse in flexible multibody dynamics. It is found that the traditionaldeformation field fails to produce an elastic rotation matrix that iscomplete to second-order in the deformation variables. A completesecond-order deformation field is proposed along with the equationsneeded to incorporate the beam model into a graph-theoretic formulationfor flexible multibody dynamics [1]. This beam modeland formulation have been implemented in a symbolic computer programcalled DynaFlex that can use Taylor, Chebyshev, or Legendrepolynomials as the basis functions in a Rayleigh–Ritz discretizationof the beam's deformation variables. To demonstrate the effects of the proposed second-order deformationfield on the response of a flexible multibody system,two examples are presented.

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