Imperfection-sensitivity analysis by using classical and catastrophe theory methods

Abstract

Comparison of the classical methods and the tools of the catastrophe theory is presented through the imperfection-sensitivity analysis of the classical stable-symmetric bifurcation problem. Generally, classical global methods are related to a large interval, while catastrophe theory concerns the neighborhood of the critical point only, being a local method. Unfortunately, in most cases of practical problems, by using classical global methods, there can hardly be obtained analytical solutions for the multivalued imperfection-sensitivity functions and the associated highly folded imperfection-sensitivity surfaces. In this paper, an approximate solution based on the catastrophe theory is presented, in comparison with the exact solution obtained in graphical way. It will be shown that by considering the problem as an imperfect version (at a fixed imperfection) of a higher order catastrophe, a topologically good solution can be obtained in a considerably large, quasi in a nonlocal domain.