Mode Interaction in Structures - An Overview

Koiter [1]was the rst to formulate an asymptotic expansion to investigate postbuckling behavior and imperfection sensitivity of elastic structures. Since then, a large number of analyses of particular structures have appeared as well as some new expansions aimed at speci c problems, such as interaction between buckling modes associated with simultaneous or nearly simultaneous buckling modes. In this contribution, various methods of this kind are discussed and compared as regards applicability and ease of use. Focus will be on Koiter's slowly varying local mode amplitude [2] and [3], on Byskov & Hutchinson's expansion [4] and on Peek & Kheyrkhahan's method [5], which enlarged the scope of the previous expansions in that it covers nonlinear prebuckling states, also. Other important contributions a number of which are based on these methods are also discussed. On the other hand, many important works, e.g. the comprehensive paper by Hunt [6] will not be mentioned in any detail. The accuracy of the methods as well as their mathematical complexity and ease of use are compared. Finally, in view of today's inexpensive and powerful computers, an obvious question is concerned with whether full analyses must always be preferred because asymptotic expansions are obsolete.

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