Keywords: prestressed cable-strut structures, pretension process, rigid-body motion, elastic deflection, multi-body system dynamics.

Flexible cable-strut structures, such as cable-dome and cable-nets, are special space structures, whose stiffnesses are completely provided by pretension, and their shape maintained also by pretension. The structures gradually obtain stiffness during the prestress process, and their final configurations and stiffness are process-dependent. Hence two problems present: first, whether the desired shape and stiffness is realizable for the reason that the result is process-dependent; second, the behaviour of the structures during the process may cause concern. However, these problems have not been solved so far.

Different from other structures, the members of flexible cable-strut structures simultaneously undergo large rigid-body motion and relatively small elastic deflection during the pretension process. The traditional finite-element-method based on displacement can only be applied to kinematically determinate structures and is incapable of this kind of problem for the existence of rigid-body motion. For the first time, based on flexible multi-body system dynamics, this paper builds up the dynamics model of cable-strut member using a relative description method. A moving reference coordinate system is used to describe the rigid-body motion and the small elastic deflection is measured in the moving reference coordinate system. The concurrent mass dynamics model of a cable-strut member is introduced, and the dynamics control equations, also the geometric constraints equations, are derived in this paper.

The method of this paper simultaneously considers the large rigid-body motion and small elastic deflection, including their coupling effects. It is applicable to the conditions with or without rigid-body motion, and its performance is not shaded by the extent of the rigid-body motion. When the rigid-body motion is excluded from the structures, the problem degenerates into one of the ordinary structure dynamics, and the solution of this paper is precisely consistent with that of the latter. During the construction, the pretension is always slowly applied, so the dynamic responses of the structures are generally negligible. Thus the quasi-static computation based on the control equations is quite reasonable. The complete motion path and the final configuration, also the final prestress distribution, can be readily found through quasi-static computation. It is interesting that the stable and unstable static equilibrium configurations can be distinguished in the quasi-static computation.

Three numerical examples are carefully made in this paper, which are the motion path computation of a four-bar mechanism, the prestress process simulations of a Geiger-style cable-dome and a tent-like cable-net, respectively. The results demonstrate the powerful capability and the high precision of the method.

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