On convex models of uncertainty for small initial imperfections of non-linear structures

We study the effect of initial geometrical imperfections on an non-linear structure at a simple critical limit point. We derive expressions for the maximum reduction of the critical load, when the uncertainty in the initial geometrical imperfections is described by a convex model. We show that seemingly small changes in the model of the imperfection-uncertainty can result in substantial changes in the predicted maximum critical-load reduction. It is therefore important to use an uncertainty model which can abe validated. Often, only limited information is available with which to formulate the uncertainty-model of the initial imperfections. Convex models describe uncertainty without employing or implying any likelihood or frequency information. A convex model of uncertainty can be formulated in a manner which is consistent with very limited information about the initial imperfections. A range of different convex models is discussed for representation of the uncertainty in the initial geometrical imperfections of a structure.