Abstract
An efficient group-theoretic method is proposed for the buckling analysis of symmetric prestressed space structures. Tangent stiffness matrices and geometric stiffness matrices of trusses, cables, and frames are given, and thus, the proposed method is applicable not only to pin-jointed structures but also to more general structures with frame and cable elements. Important contribution of initial prestresses is considered in formulating the tangent stiffness matrices for the prestressed structures. By adopting irreducible representations of a symmetry group and projection operator theory, the associated stiffness matrices are converted to symmetry-adapted forms. Subsequently, the original buckling problem is decomposed into a series of independent subproblems with smaller dimensions, which obtain precise solutions but lead to significant reduction in computational cost. To describe the typical process for the group-theoretic method, efficient buckling analyses on four types of symmetric prestressed space structures composed of cables, trusses, and/or frames are carried out. The computational efficiency of the proposed method is dramatically improved in comparison with those of FEM and the conventional numerical method. Comparing the results with the corresponding ones from ABAQUS and published data, we verify that the proposed method is elegant and reliable.
Similar content being viewed by others
References
Kitipornchai S., Kang W.J., Lam H.F., Albermani F.: Factors affecting the design and construction of Lamella suspen-dome systems. J. Constr. Steel Res. 61, 764–785 (2005)
Ohsaki M., Zhang J.Y.: Stability conditions of prestressed pin-jointed structures. Int. J. Nonlinear Mech. 41, 1109–1117 (2006)
Chen, Y., Feng, J., Zhuang, L., Xia, S.: Elastic stability of symmetric dome structures using group theory. In: Earth and space 2012@struction, and Operations in Challenging Environments, ASCE (2012)
Timoshenko S.P., Gere J.M.: Theory of Elastic Stability. McGraw-Hill, New York (1961)
Ikeda K., Murota K., Yanagimoto A., Noguchi H.: Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization. Comput. Methods Appl. M. 196, 1648–1661 (2007)
Kang W.J., Chen Z.H., Lam H.F., Zuo C.R.: Analysis and design of the general and outmost-ring stiffened suspen-dome structures. Eng. Struct. 25, 1685–1695 (2003)
Ragavan V., Amde A.M.: Nonlinear buckling and postbuckling of cable-stiffened prestressed domes. ASCE J. Eng. Mech. 125, 1164–1172 (1999)
Lazopoulos K.A.: Stability of an elastic cytoskeletal tensegrity model. Int. J. Solids Struct. 42, 3459–3469 (2005)
Trefethen, L.N., Bau III, D.: Numerical Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics (1997)
Mohan S.J., Pratap R.: A group theoretic approach to the linear free vibration analysis of shells with dihedral symmetry. J. Sound Vib. 252, 317–341 (2002)
Kaveh A., Fazli H.: Graph coloration and group theory in dynamic analysis of symmetric finite element models. Finite Element Anal. Des. 43, 901–911 (2007)
Kaveh A., Rahami H., Nikbakht M.: Vibration analysis of regular structures by graph products: cable networks. Comput. Struct. 88, 588–601 (2010)
Kaveh A., Nikbakht M., Rahami H.: Improved group theoretic method using graph products for the analysis of symmetric-regular structures. Acta Mech. 210, 265–289 (2010)
Shojaei I., Kaveh A., Rahami H.: Analysis of structures convertible to repeated structures using graph products. Comput. Struct. 125, 153–163 (2013)
Kaveh A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Springer, GmbH, Wien, New York (2013)
Kaveh A., Nikbakht M.: Analysis of space towers using combined symmetry groups and product graphs. Acta Mech. 218, 133–160 (2011)
Chen Y., Feng J.: Generalized eigenvalue analysis of symmetric prestressed structures using group theory. ASCE J. Comput. Civil Eng. 26, 488–497 (2012)
Altmann S.L., Herzig P.: Point-Group Theory Tables. Clarendon Press, Oxford (1994)
Zingoni A.: A group-theoretic formulation for symmetric finite elements. Finite Element Anal. Des. 41, 615–635 (2005)
Zingoni A.: Group-theoretic exploitations of symmetry in computational solid and structural mechanics. Int. J. Numer. Methods Eng. 79, 253–289 (2009)
Healey T.J.: A group-theoretic approach to computational bifurcation problems with symmetry. Comput. Methods Appl. Mech. 67, 257–295 (1988)
Ikeda K., Murota K.: Bifurcation analysis of symmetric structures using block-diagonalization. Comput. Methods Appl. Mech. 86, 215–243 (1991)
Wohlever J.C., Healey T.J.: A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell. Comput. Methods Appl. Mech. 122, 315–349 (1995)
Kaveh A., Nikbakht M.: Stability analysis of hyper symmetric skeletal structures using group theory. Acta Mech. 200, 177–197 (2008)
Koohestani K., Kaveh A.: Efficient buckling and free vibration analysis of cyclically repeated space truss structures. Finite Element Anal. Des. 46, 943–948 (2010)
Koohestani K., Guest S.D.: A new approach to the analytical and numerical form-finding of tensegrity structures. Int. J. Solids Struct. 50, 2995–3007 (2013)
Chen Y., Feng J., Wu Y.: Novel form-finding of tensegrity structures using ant colony systems. J. Mech. Robot. Trans. ASME 4, 310011–310017 (2012)
Chen Y., Feng J., Wu Y.: Prestress stability of pin-jointed assemblies using ant colony systems. Mech. Res. Commun. 41, 30–36 (2012)
Vassart N., Laporte R., Motro R.: Determination of mechanism’s order for kinematically and statically indetermined systems. Int. J. Solids Struct. 37, 3807–3839 (2000)
Guest S.D.: The stiffness of tensegrity structures. IMA J. Appl. Math. 76, 57–66 (2011)
Guest S.D.: The stiffness of prestressed frameworks: a unifying approach. Int. J. Solids Struct. 43, 842–854 (2006)
Torkamani M.A., Shieh J.: Higher-order stiffness matrices in nonlinear finite element analysis of plane truss structures. Eng. Struct. 33, 3516–3526 (2011)
Chang J.: Derivation of the geometric stiffness matrix of a truss element from a simple physical concept. J. Int. Assoc. Shell Spat. Struct. 45, 22–28 (2004)
Yang Y., McGuire W.: Stiffness matrix for geometric nonlinear analysis. J. Struct. Eng. 112, 853–877 (1986)
Kattan P.I.: MATLAB Guide to Finite Elements: An Interactive Approach. Springer, Berlin (2007)
Zienkiewicz O.C., Taylor R.L.: The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann, London (2005)
Geiger, D.H.: Roof Structure. US Patent No. 4736553 (1988)
Geiger, D.H., Stefaniuk, A., Chen, D.: The design and construction of two cable domes for the Korean Olympics. In: Proceedings of the IASS Symposium on Shells, Membranes and Space Frames. Osaka: Elsevier Science Publishers BV (1986)
Kawaguchi M., Tatemichi I., Chen P.S.: Optimum shapes of a cable dome structure. Eng. Struct. 21, 719–725 (1999)
Kawaguchi M., Abe M., Tatemichi I.: Design, tests and realization of suspen-dome system. J. Int. Assoc. Shell Spat. Struct. 40, 179–192 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, Y., Feng, J. Group-theoretic method for efficient buckling analysis of prestressed space structures. Acta Mech 226, 957–973 (2015). https://doi.org/10.1007/s00707-014-1234-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-014-1234-x