Keywords: complementary-slackness system, Gaussian principle, artificial neural network, guyed mast, ship-like body.

The study on nonsmooth behavior for cable-structures may date back to the 1970s. In 1976, Panagitopoulos had dealt with the inelastic, stress-unilateral analysis of cable-structures undergoing large displacements, and considered inequality problems. His work established the mathematic basis of modeling cable-structures. The analysis of cable-structures may be included in the complementarity problems [1]. But most of the study was concentrated on static or quasi-static problems.

Nonsmooth mechanics allows a general theoretical description but relevant problems must be solved numerically. In spite of many value contributions to the numerical methods for non-continuous systems the existing algorithms are still extremely time-consuming [2]. Therefore the numerical solution of all kinds of complementarity problems is a topic of current research.

In the present paper, cable-structures have been considered as two classes of mechanical complementary-slackness systems. Based on the optimization algorithms for multi-body dynamics with unilateral contacts, an algorithm using an artificial neural network has been developed. First, the complementarity problems for those structures has been formulated; then using a generalized Gaussian least action principle they have been summarized as an optimization problem [3]. Based on Hopfield's work [4], an artificial neural network has been designed and used to decide the combination of possible constraints at each step in a simulation. As examples, two cable-structures have been investigated. An example of a guyed mast shows the suitability of the proposed method for practical cable-structures. As second example, two ship-like bodies connected by six cables and excited by waves have been studied. The cables might be under tension, or they might be slack, thus forming a unilateral system generating possible impacts. The results of a numerical calculation compare reasonably well with experiments.

Through the analysis of two examples, the following conclusions can be drawn:

1. The loosening phenomenon of some cables may occur when the design of structures with cables is not reasonable.
2. In modeling of cable-structures, consideration of the non-smooth behavior of those systems has been found to be necessary.
3. The artificial neural networks used to analyze the dynamic systems with unilateral constraints can save a significant amount of computer time.

1

Q. Feng, J. Tu, "Modeling and Algorithm on Class of Mechanical Systems with Unilateral Constraints", Arch Appl. Mech., Vol.76, 103-116, 2006. doi:10.1007/s00419-006-0008-x

2

K.G. Murty, "Linear Complementarity, Linear and Nonlinear Programming", Sigma Series in Applied Mathematics (ed. D.J. White), Heldermann Verlag, Berlin, 1988.

3

B. Brogliato, "Nonsmooth Mechanics", Springer, London, 1999.

4

M.T. Hagan, H.B. Demuth, M. Beale, "Neural Network Design", PWS Publishing Company, 1996.

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