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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 87

Modeling a Class of Mechanical Complementary-Slackness Systems

Q. Feng1 and R.Y. Shen2

1School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, P.R. China
2State Key Laboratory of Mechanical System and Vibration, Jiaotong University, Shanghai, P.R. China

Full Bibliographic Reference for this paper
Q. Feng, R.Y. Shen, "Modeling a Class of Mechanical Complementary-Slackness Systems", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 87, 2008. doi:10.4203/ccp.88.87
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.

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
K.G. Murty, "Linear Complementarity, Linear and Nonlinear Programming", Sigma Series in Applied Mathematics (ed. D.J. White), Heldermann Verlag, Berlin, 1988.
B. Brogliato, "Nonsmooth Mechanics", Springer, London, 1999.
M.T. Hagan, H.B. Demuth, M. Beale, "Neural Network Design", PWS Publishing Company, 1996.

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