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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 174
A High Performance Algorithm to solve the Static Stiffness Problem of a Catenary A. Alberto1, E. Arias2, D. Cebrian1, T. Rojo2, F. Cuartero2 and J. Benet2
1Albacete Computer Science Research Institute, Spain
Full Bibliographic Reference for this paper
A. Alberto, E. Arias, D. Cebrian, T. Rojo, F. Cuartero, J. Benet, "A High Performance Algorithm to solve the Static Stiffness Problem of a Catenary", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 174, 2006. doi:10.4203/ccp.83.174
Keywords: structure catenary, static stiffness problem, interaction pantograph-catenary, equilibrium equation, high performance computing, software tool.
Summary
In this paper, we will present a high performance implementation
that has been carried out on various algorithms to solve the
equilibrium equation of the system in a catenary model, using
spans with different numbers of droppers and different positions.
The implementations have been performed both for the continued and
stitched structure of the catenary.
In the static problem the static position of
the system is determined when we apply a vertical force over the contact
wire. Thus, it is necessary to configurate the stiffness matrix Once the equation that determines the position of every node forming the structure of the catenary has been solved, it is necessary to tackle another study that will produce an iterative process. By taking a point inside the first span we exercise a vertical force on the contact wire, so that we must solve the equilibrium equation again, to obtain the new position of every node inside the structure of the catenary. This process is iterated for several points inside every span. Once the study has been performed inside the first span, the same process has to be repeated for each of the remainig spans. Most of the execution time is spent in solving this problem. Thus, it is important to bring about a reduction related to the storage requirements, such as in the execution time. We have used iterative methods with preconditioning for the resolution of this system [1]. It has been chosen both from the precision and from the time of calculation. A second advantage of these implementations can be taken into account, which is the considerable saving of storage memory requirements obtained.
The stiffness matrix The original algorithms stored the stiffness matrix in dense format, thus, they had large memory storage requirements. The high performance algorithms store the same matrix but in sparse format, and this reduces the memory requirements, and benefits the efficiency of the algorithms. The execution time has also been drastically reduced compared to the original implementation. All these algorithms have been used as part of a user-friendly, interactive and graphically oriented software tool, wich is currently being used in the industry. References
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