Abstract
The loss of stability of a general conservative structural system described by n generalized coordinates, a loading parameter, and an imperfection parameter, is studied. Attention is restricted to discrete critical points of the ‘perfect’ system and three branching points which might be described as asymmetric, stable-symmetric and unstable-symmetric are examined in detail. For each point explicit expressions for the derivatives of the post-buckling path of the ‘perfect’ system and for the derivatives relating the critical load of an ‘imperfect’ system to the magnitude of the imperfection parameter are derived intrinsically, without resort to power-series expansions. The general theory is finally applied to three ‘models’ designed to illustrate the salient features of the three branching points under consideration.
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