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PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and M. Papadrakakis
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
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 . 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 . 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 . Based on Hopfield's work , 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:
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