Asymptotic and probabilistic approach to buckling of structures and materials

Kiyohiro Ikeda, Kazuo Murota

Research output: Contribution to journalReview articlepeer-review

6 Citations (Scopus)


The general theory of elastic stability invented by Koiter (1945, "On the Stability of Elastic Equilibrium," Ph.D. thesis, Delft, Holland) motivated the development of a series of asymptotic approaches to deal with the initial postbuckling behavior of structures. These approaches, which played a pivotal role in the precomputer age, are somewhat overshadowed by the progress of computational environment. Recently, the importance of the asymptotic approaches has been revived through the extension of their theoretical background and the combination with the framework of finite element method and with group-theoretic bifurcation theory in nonlinear mathematics. The approaches serve as an efficient and insightful strategy to tackle probabilistic scatter of critical loads. We review, through the perspective of theoretical engineers, the historical development and recent revival of the asymptotic approaches for buckling of imperfection-sensitive structures and materials.

Original languageEnglish
Pages (from-to)408011-4080116
Number of pages3672106
JournalApplied Mechanics Reviews
Issue number1-6
Publication statusPublished - 2008 Jan
Externally publishedYes

ASJC Scopus subject areas

  • Mechanical Engineering


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