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Analysis of space truss towers using combined symmetry groups and product graphs

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Abstract

In this paper, a modified group theoretic method is introduced for symmetry analysis of regular structures. A structure is called regular if its model can be formed by one of the graph products. Here, the concepts from graph products are used in order to simplify the conventional group theoretic analysis of cyclically symmetric structures. The analysis of truss towers under static loads is presented for simple first-order, and geometrically nonlinear second-order effects.

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References

  1. Kaveh A., Sayarinejad M.A.: Eigensolutions for matrices of special patterns. Comm. Numer. Methods Eng. 19, 125–136 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Kaveh A., Sayarinejad M.A.: Eigenvalues of factorable matrices with form IV symmetry. Comm. Numer. Methods Eng. 21, 269–278 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kaveh A.: Structural Mechanics: Graph and Matrix Methods, 3rd edn. Research Studies Press, Somerset (2004)

    Google Scholar 

  4. Kaveh A., Salimbahrami B.: Eigensolutions of symmetric frames using graph factorization. Comm. Numer. Methods Eng. 20, 889–910 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Thomas D.L.: Dynamics of rotationally periodic structures. Int. J. Numer. Methods Eng. 14, 81–102 (1979)

    Article  MATH  Google Scholar 

  6. Williams F.W.: An algorithm for exact eigenvalue calculations for rotationally periodic structures. Int. J. Numer. Methods Eng. 23, 609–622 (1986)

    Article  MATH  Google Scholar 

  7. Williams F.W.: Exact eigenvalue calculations for rotationally periodic sub-structures. Int. J. Numer. Methods Eng. 23, 695–706 (1989)

    Article  Google Scholar 

  8. Hasan M.A., Hasan J.A.K.: Block eigenvalue decomposition using nth roots of identity matrix. 41st IEEE Conf. Decis. Control 2, 2119–2124 (2002)

    MathSciNet  Google Scholar 

  9. Kaveh A., Rahami H.: An efficient method for decomposition of regular structures using graph products. Int. J. Numer. Methods Eng. 61, 1718–1797 (2004)

    MathSciNet  Google Scholar 

  10. Kaveh A., Rahami H.: Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics. Int. J. Numer. Methods Eng. 6, 833–863 (2006)

    MathSciNet  Google Scholar 

  11. Kangwai R.D., Guest S.D., Pellegrino S.: An introduction to the analysis of symmetric structures. Comput. Struct. 71, 671–688 (1999)

    Article  MathSciNet  Google Scholar 

  12. Zloković G.M.: Group Theory and G-vector Spaces in Engineering Structures, Vibration, Stability and Statics. Ellis Horwood, Chichester (1989)

    Google Scholar 

  13. Zingoni A.: An efficient computational scheme for the vibration analysis of high-tension cable nets. J Sound Vib 189, 55–79 (1996)

    Article  Google Scholar 

  14. Zingoni A.: Group-theoretic exploitations of symmetry in solid and structural mechanics. Int. J. Numer. Methods Eng. 79, 253–289 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zingoni A.: On the symmetries and vibration modes of layered space grids. Eng. Struct. 27, 629–638 (2005)

    Article  Google Scholar 

  16. Zingoni A.: A group-theoretic formulation for symmetric finite elements. Finite Elem. Anal. Des. 41, 615–635 (2006)

    Article  MathSciNet  Google Scholar 

  17. Zingoni A.: On group-theoretic computation of natural frequencies for spring-mass dynamic systems with rectilinear motion. Commun. Numer. Methods Eng. 24, 973–987 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kaveh A., Nikbakht M.: Block diagonalization of Laplacian matrices of symmetric graphs via group theory. Int. J. Numer. Methods Eng. 69, 908–947 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Kaveh A., Nikbakht M.: Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory. Adv. Eng. Softw. 41, 22–31 (2010)

    Article  MATH  Google Scholar 

  20. Kaveh A., Nikbakht M.: Buckling load of symmetric plane frames using canonical forms and group theory. Acta Mech. 185, 89–128 (2006)

    Article  MATH  Google Scholar 

  21. Kaveh A., Nikbakht M.: Stability analysis of hyper symmetric skeletal structures using group theory. Acta Mech. 200, 177–197 (2008)

    Article  MATH  Google Scholar 

  22. Kaveh A., Nikbakht M.: Decomposition of symmetric mass-spring vibrating systems using groups, graphs, and linear algebra. Commun. Numer. Methods Eng. 23, 639–664 (2006)

    Article  MathSciNet  Google Scholar 

  23. Kaveh, A., Nikbakht, M.: Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory. In: Topping, B.H.V., Montero, G., Montenegro, R. (eds.) Proceedings of the 8th International Conference on Computational Structures Technology. Civil-Comp Press, Stirlingshire (2006)

  24. Kaveh, A., Nikbakht, M.: Applications of group and graph products in configuration processing of symmetric structures. In: The 9th International Conference on Computational Structures Technology, Athens, 2–5 Sept 2008

  25. Sabidussi G.: Graph multiplication. Math. Z. 72, 446–457 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  26. Weichsel P.M.: The Kronecker product of graphs. Proc. Am. Math. Soc. 13, 47–52 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  27. Harary F., Wilcox G.W.: Boolean operations on graphs. Math. Scand. 20, 41–51 (1967)

    MATH  MathSciNet  Google Scholar 

  28. Hammermesh M.: Group Theory and its Application to Physical Problems. Dover, New York (1962)

    Google Scholar 

  29. Albert Cotton F.: Chemical Applications of Group Theory. Wiley, New York (1990)

    Google Scholar 

  30. Armstrong M.A.: Groups and Symmetry. Springer, New York (1988)

    MATH  Google Scholar 

  31. Miller W. Jr: Symmetry Groups and Their Applications. Academic Press, New York (1972)

    MATH  Google Scholar 

  32. Healey T.J., Treacy J.A.: Exact block diagonalization of large eigenvalue problems for structures with symmetry. Int. J. Numer. Methods Eng. 31, 265–285 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  33. Kaveh A., Nikbakht M., Rahami H.: Improved group theoretic method using graphs products, for the analysis of symmetric-regular structures. Acta Mech. 210, 265–289 (2010)

    Article  MATH  Google Scholar 

  34. Zingoni A., Pavlovic M.N., Zlokovic G.M.: A symmetry-adapted flexibility approach for multi-storey space frames: symmetry-adapted loads. Struct. Eng. Rev. 7, 121–130 (1995)

    Google Scholar 

  35. Kardestuncer H.: Elementary Matrix Analysis of Structures. McGraw-Hill, New York (1974)

    Google Scholar 

  36. Ghali A., Neville A.M., Brown T.G.: Structural Analysis: A Unified Classical and Matrix Approach. E. & FN Spon, London, UK (2003)

    Google Scholar 

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Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran 16, Iran

    A. Kaveh & M. Nikbakht

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  1. A. Kaveh
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  2. M. Nikbakht
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Correspondence to A. Kaveh.

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Kaveh, A., Nikbakht, M. Analysis of space truss towers using combined symmetry groups and product graphs. Acta Mech 218, 133–160 (2011). https://doi.org/10.1007/s00707-010-0411-9

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  • DOI: https://doi.org/10.1007/s00707-010-0411-9

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