Maximum loads of imperfect systems corresponding to stable bifurcation

Asimple and computationally inexpensive approach is presented for obtaining the maximum load factor of an elastic structure considering reduction of load-carrying capacity due to inevitable initial imperfections. The structure has a stable bifurcation point if no initial imperfection exists. An antioptimization problem is formulated for minimizing the maximum loads reduced by the most sensitive imperfection within the convex bounds on the imperfections of nodal locations and nodal loads. The maximum loads may be defined by bifurcation points or deformation constraints. A problem of simultaneous analysis and design with energy method is formulated to avoid laborious nonlinear pathfollowing analysis. The stable bifurcation point is located by minimizing the load factor under constraint on the lowest eigenvalue of the stability matrix. It is shown in the examples that a minor imperfection that is usually dismissed is very important in evaluating the maximum load of a flexible structure