Elastic postbuckling with nonlinear constraint

Koiter’s asymptotic theory of initial postbuckling and imperfection sensitivity of elastic structures is expanded such that almost any auxiliary condition can be handled directly. The theory, which employs Lagrange multiplier techniques, is valid for strain measures that are quadratic in the displacements, i.e. it is exact for Lugrangiun strain measures, and auxiliary conditions and loadings that are quartic in their arguments. Although the general formulas are rather lengthy and complicated in the general case they simplify considerably in almost all cases of practical interest. Frequently the formulas are only slightly more complex than in the equivalent situation without auxiliary conditions. The method is applied to the example of an elastic inextensible circular ring but is suitable for all elastic structures which comply with the above mentioned requirements regarding strain measure and auxiliary conditions. Copyright 0 1996 Elsevier Science Ltd