Critical Imperfection Territory∗

The critical limit load of elastic structures can decrease due to the effect of unavoidable imperfections. The “critical imperfection territory” covers all imperfections resulting in a value of the critical load that is smaller than a prescribed value. These territories are determined with the help of a potential function and by using results of catastrophe theory. General rules for their determination are outlined and the specific critical imperfection territories are shown for the most important cases (fold, cusp, and elliptic and hyperbolic umbilic catastrophes). These territories give information similar to that given by imperfection-sensitivity surfaces, but they use a space of one less dimension.