Abstract
By means of the theory of universal unfolding, the influence of multiimperfections upon the critical load of structure in engineering is analysed in this paper. For the pitchfork problem, a lower bound of increments of the critical loads caused by imperfections of the structures is given. A simple and available numerical method for computing the lower bound is described.
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Thomson J M T, Hunt G W.A General Theory of Elastic Stability[M]. New York: John Wiley, 1973.
Hunt G W. Imperfection sensitivity of semi-symmetric branching[J].Proc Royal Soc London, Ser A 1977,357(2):193–211.
Koiter W T. On the stability of elastic equilibrium [D]. Ph D dissertation. English translation, Delft Holland: NASA Technical translation, 1967,F10:833.
Niwa Y, Watanabe E, Nakagawa N. Catastrophe and imperfection sensitivity of two-degree-of freedom systems[J].Proc Japan Soc Civil Engineers, 1981,307(1):99–111.
Kirkpatrick S W, Holmen B S. Effects of initial imperfections on dynamic buckling of shells[J].J Engrg Mech Div, 1988,115(5):1025–1093.
Elishakoff I. Stochastic simulation of an initial imperfection data bank for isotropic shell with general inperfections[A]. In: I Elishakoff et al eds.Buckling of Structures[C]. Amsterdam: Elsevier, 1988,195–209.
Lindberg H E. Random imperfections for dynamic pulse buckling[J].J Engrg Mech Div, 1988,114(6):1144–1165.
Murota K, Ikada K. Critical initial imperfection of structures[J].Int J Solid Struct, 1990,26(8):865–886.
Murota K, Ikada K. Critical imperfection of symmetric structures[J].SIAM Appl Math, 1991,51(5):1222–1254.
Golubitsky M, Schaeffer D G.Singularities and Groups in Bifurcation Theory[M]. Vol.1, Berlin Heidelberg, New York, Tokyo: Springer-Verlag, 1984.
Arnold V I. Singularity theory [J].London Math Soc Lecture Note Series,51, Berlin Heidelberg, New York, Tokyo: Springer-Verlag, 1981.
Chow S N, Hale J K, Mallet-Paret J. Application of generic bifurcations[J].Arch Rat Mech Anal, 1975,59(2):159–188.
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Communicated by Chien Weizang
Foundation item: the National Nature Science Foundation of China (19371039)
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Zhengyou, Z., Yuhao, C. The influence of imperfections upon the critical load of structures. Appl Math Mech 20, 1108–1115 (1999). https://doi.org/10.1007/BF02460327
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DOI: https://doi.org/10.1007/BF02460327