预扭对大挠度柔性梁变形影响的非线性分析

Nonlinear analysis of the effects of pretwisted angles on the deformation of flexible beams under large deflection

利用Green-Lagrange应变张量建立了梁在大挠度、大转动、小应变条件下的预扭角与变形位移之间的联系,并根据Hamilton原理得到了梁运动的有限元方程,研究了预扭角变化对大挠度柔性梁变形的影响。数值结果表明:预扭角的变化对梁的侧向变形的影响最大、横向变形的影响次之,对弹性扭转角影响最小。通过梁运动的有限元模型对大挠度柔性梁施加的预扭角可以计算梁的变形。

Relations of pretwisted angles between deformation displacements which are valid for flexible beams under arbitrarily large displacements and rotations,but small strains are presented using the Green-Lagrange strain tensors.The finite element equtions of flexible beams motion are derived according to Hamilton＇s principle.The effects of pretwisted Angles on the deformation of flexible beams under large deflection are inverstigated.The numerical results show pretwisted angles change transverse deformations of flexible beams the more greatly than lateral deformations,change twist angles of flexible beams little.The deformations of pretwisted beams can be calculated successfully by these models.