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THE METHOD OF SOLVING UNSTABLE EQUILIBRIUM STATES OF CABLE-NET STRUCTURES
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摘要: 索网结构的施工张拉成形过程是不稳定平衡状态求解过程,在此过程中机构和弹性位移相互耦合。基于索无应力长度,采用解析抛物线索单元,考虑弹性变形和张力关系;利用铰接体系平衡矩阵理论求解节点不平衡力向量,避免机构刚度矩阵奇异求解难题;最后,用动力松弛法求解将这一耦合问题解耦。算例表明,该方法能求解张力结构成形过程中的不稳定平衡状态,且通过改变主动索无应力长度可模拟施工张拉成形过程;当无节点荷载或节点荷载很小时,抛物线单元与杆单元分析差别较大,表明采用抛物线索单元是合理的。Abstract: The tension forming process of cable-net structures in construction is the process of solving unstable equilibriums,in which the mechanism and elastic deformation are coupled.On the basis of unstressed cable length,an analytical parabolic cable element is used to consider the elastic tension and deformation.The unbalanced nodal force vector is evaluated by using the equilibrium matrix theory of the pin joint system,which avoids solving the singular stiffness matrix of a mechanism.The dynamical relaxation method is used to solve the nonlinear equation by making the coupling problem decoupled.Numerical examples indicate that the proposed algorithm is capable of solving the unstable equilibrium and simulating the tension forming process in construction by changing the unstressed length of active cables.When there is no load or the load is small,the analytical results of employing parabolic elements and link elements are significantly different,which shows the fidelity of parabolic cable elements.
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Key words:
- cable-net /
- dynamic relaxation /
- unstable equilibrium /
- parabolic cable element
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