- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 510180, 16 pages
Graph Products and Its Applications in Mathematical Formulation of Structures
1Department of Structural Engineering, Islamic Azad University, Shabestar Branch, Shabestar, Iran
2Marand Faculty of Engineering, University of Tabriz, Tabriz 51667 71719, Iran
3Department of Mathematics, Islamic Azad University, Shabestar Branch, Shabestar, Iran
Received 15 June 2012; Revised 15 October 2012; Accepted 16 October 2012
Academic Editor: C. Conca
Copyright © 2012 M. Nouri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- H. Nooshin, “Algebraic representation and processing of structural configurations,” Computers and Structures, vol. 5, no. 2-3, pp. 119–130, 1975.
- H. Nooshin, P. Disney, and C. Yamamoto, Formian, Multi-Science Publishers, Essex, UK, 1993.
- H. Nooshin and P. Disney, “Formex configuration processing III,” International Journal of Space Structures, vol. 17, no. 1, pp. 1–50, 2002.
- A. Behravesh, A. Kaveh, M. Nani, and S. Sabet, “A set theoretical approach for configuration processing,” Computers & Structures, vol. 30, no. 6, pp. 1293–1302, 1988.
- A. Kaveh, “A graph-theoretical approach to configuration processing,” Computers and Structures, vol. 48, no. 2, pp. 357–363, 1993.
- A. Kaveh, X. Jia, and Q. Weng, “Rotation as a general operation for configuration processing,” Scientia Iranica, vol. 17, no. 2, pp. 131–140, 2010.
- A. Kaveh, Optimal Structural Analysis, John Wiley & Sons, Somerset, UK, 2nd edition, 2006.
- A. Kaveh and H. Rahami, “An efficient method for decomposition of regular structures using graph products,” International Journal for Numerical Methods in Engineering, vol. 61, no. 11, pp. 1797–1808, 2004.
- A. Kaveh and K. Koohestani, “Graph products for configuration processing of space structures,” Computers and Structures, vol. 86, no. 11-12, pp. 1219–1231, 2008.
- A. Kaveh and M. Nouri, “Weighted graph products for configuration processing of planar and space structures,” International Journal of Space Structures, vol. 24, no. 1, pp. 13–26, 2009.
- A. Kaveh and S. Beheshti, “Weighted triangular and circular graph products for configuration processing,” Periodica Polytechnica, vol. 56, pp. 1–9, 2012.
- W. C. Thacker, “A brief review of techniques for generating irregular computational grids,” International Journal for Numerical Methods in Engineering, vol. 15, no. 9, pp. 1335–1341, 1980.
- J. F. Thompson, Z. U. A. Warsi, and C. W. Mastin, Numerical Grid Generation, Foundations and Applications, Elsevier, Amsterdam, The Netherlands, 1985.
- V. D. Liseikin, Grid Gneration Methods, Scientific Computation, Springer, Berlin, Germany, 1999.
- B. H. V. Topping, J. Muylle, and P. Ivanyi, Finite Element Mesh Generation, Saxe Coburg, Pubn, UK, 2004.
- W. Imrich and S. Klavžar, Product Graphs, Structure and Recognition, Wiley-Interscience, New York, NY, USA, 2000.
- A. Kaveh and H. Rahami, “A unified method for eigendecomposition of graph products,” Communications in Numerical Methods in Engineering, vol. 21, no. 7, pp. 377–388, 2005.
- A. Kaveh, M. Nikbakht, and H. Rahami, “Improved group theoretic method using graph products for the analysis of symmetric-regular structures,” Acta Mechanica, vol. 210, no. 3-4, pp. 265–289, 2010.
- A. Kaveh and H. Rahami, “An efficient analysis of repetitive structures generated by graph products,” International Journal for Numerical Methods in Engineering, vol. 84, no. 1, pp. 108–126, 2010.
- A. Kaveh, Structural Mechanics: Graph and Matrix Methods, Research Studies Press, Somerset, UK, 3rd edition, 2004.