Elastodynamic analysis of low tension cables using a new curved beam element
Elastodynamic analysis of low tension cables using a new curved beam element
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DOI：
10.1016/j.ijsolstr.2005.03.053
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发表时间：
2006-03
影响因子：
3.6
通讯作者：
Zheng Hong Zhu;S. Meguid
中科院分区：
文献类型：
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作者：
Zheng Hong Zhu;S. Meguid
在本文中，我们解决并克服了使用经典的电缆理论来处理低张力电缆的困难，通过开发一个新的三节点锁定自由非线性曲梁单元。基于非线性广义曲梁理论，新单元的大变形和大转角均采用Updated Lagrangian格式。采用相容耦合的多项式位移场来满足膜锁自由条件和能够恢复不可伸长弯曲模态的要求。五次横向位移插值函数被用来表示梁的弯曲变形，而轴向和扭转位移场是由假定的线性膜和扭转剪切应变场，这是耦合到横向位移场的积分。数值结果表明，该曲梁单元具有良好的上级精度和较高的收敛速度。通过对一根带有测量装置的自由摆动钢索的松弛和低张力试验，进一步验证了该单元的稳定性和精度。实验结果与有限元预测结果吻合较好。
In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.