ON CONVEX MODELS OF UNCERTAINTY FOR SMALL INITIAL IMPERFECTIONS OF NONLINEAR STRUCTURES

We study the effect of initial geometrical imperfections on an non-lin ear structure at a simple critical limit point. We derive expressions for the maximum reduction of the critical load, when the uncertainty i n the initial geometrical imperfections is described by a convex model . We show that seemingly small changes in the model of the imperfectio n-uncertainty can result in substantial changes in the predicted maxim um critical-load reduction. It is therefore important to use an uncert ainty model which can abe validated. Often, only limited information i s available with which to formulate the uncertainty-model of the initi al imperfections. Convex models describe uncertainty without employing or implying any likelihood or frequency information. A convex model o f uncertainty can be formulated in a manner which is consistent with v ery limited information about the initial imperfections. A range of di fferent convex models is discussed for representation of the uncertain ty in the initial geometrical imperfections of a structure.