Imperfection Sensitivity Laws

  • Kiyohiro Ikeda
  • Kazuo Murota
Part of the Applied Mathematical Sciences book series (AMS, volume 149)


Initial imperfections are problematic for structural systems undergoing bifurcation in that even small imperfections can sharply reduce their strength. The classical linearized theory was inadequate to explain the experimental behavior of shells. Such inadequacy was resolved by von Kámán, Dunn, and Tsien, 1940 [186] through the implementation of nonlinearity and imperfections. The “imperfection sensitivity laws” were formulated by Koiter, 1945 [112] to explain the mechanism of such sharp reduction, and different types of bifurcation points are shown to possess different types of imperfection sensitivity. The imperfection sensitivity of simple structures was observed experimentally by Roorda, 1965 [155]. Thompson and Hunt, 1973 [174] formulated the imperfection sensitivity law of a system with a single imperfection parameter through the perturbation to the total potential energy function of the system in question. Hunt, 1977 [73] combined this approach with the catastrophe theory to determine imperfection sensitivity. Thereafter research of imperfection sensitivity has been conducted extensively (e.g., Hui, 1986 [71]; Hui and Chen 1987 [72]; Elishakoff, Li, and Starnes, 1996 [46]; Ohsaki and Nakamura, 1994 [139]; Godoy, 2000 [56]).


Limit Point Bifurcation Point Equilibrium Path Initial Imperfection Newton Polygon 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversityAoba SendaiJapan
  2. 2.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

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