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Random Imperfection (I)

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Imperfect Bifurcation in Structures and Materials

Part of the book series: Applied Mathematical Sciences ((AMS,volume 149))

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Abstract

The critical load of a structure is subject to a probabilistic scatter when it is modeled as a function of several random imperfections. This chapter offers a procedure to obtain the probability density function of the critical load for structures with a number of imperfections with known probabilistic characteristics. Chapter 3, “Imperfection Sensitivity Laws,” is a foundation of this chapter, and this chapter is extended to a system with group symmetry in Chap. 11.

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Notes

  1. 1.

    Several excellent textbooks explain this issue (e.g., Bolotin, 1969 [14], 1984 [15]; Elishakoff, 1983 [41]; Augusti, Barratta, and Casciati, 1984 [7]; Lindberg and Florence, 1987 [122]; Ben-Haim and Elishakoff, 1990 [12]; and Elishakoff, Lin, and Zhu, 1994 [42]).

  2. 2.

    For example, Roorda and Hansen, 1972 [164] extended these laws to a single-mode, normally distributed imperfection.

  3. 3.

    This chapter is based on Ikeda and Murota, 1991 [81], 1993 [82].

  4. 4.

    See, for example, Weibull, 1939 [195], 1951 [196].

  5. 5.

    See Theorem 2.1.6 of Galambos, 1978 [47]; also Kendall and Stuart, 1977 [109].

  6. 6.

    Here “inf” denotes the infimum of a set of numbers, which is defined to be the largest number that is not larger than any number in the set. Similarly, “sup” denotes the supremum of a set of numbers, which is defined to be the smallest number that is not smaller than any number in the set.

  7. 7.

    The derivations of these factors are treated in Problems 5.4–5.6.

  8. 8.

    See Chap. 14 for more issues on the bifurcation of cylindrical sand specimens.

References

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, Tohoku University, Sendai, Japan

    Kiyohiro Ikeda

  2. Department of Economics and Business Administration, Tokyo Metropolitan University, Hachioji, Japan

    Kazuo Murota

Authors
  1. Kiyohiro Ikeda
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  2. Kazuo Murota
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Ikeda, K., Murota, K. (2019). Random Imperfection (I). In: Imperfect Bifurcation in Structures and Materials. Applied Mathematical Sciences, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-030-21473-9_5

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