A comprehensive catastrophe theory for non‐linear buckling of simple systems exhibiting fold and cusp catastrophes

Abstract

SUMMARYNon-linear static buckling of simple systems associated with typical discrete critical points is comprehensively presented using elementary Catastrophe Theory. Attention is focused on the Fold and Cusp Catastrophe, all local properties of which are assessed in detail. Hence, in dealing with stability problems of potential systems there is no need to seek any of these properties since all of these are known a priori. Then, one has only to classify, after reduction, the total potential energy of a system into one of the universal unfoldings of the above types of catastrophe. Two illustrative numerical examples show the methodology of the proposed technique.

Fold Catastrophe Characteristics of Pitch Supercavitating Vehicle at Certain Depth

“…Catastrophe theory has been the main tool to solve nonlinear problems, and has achieved many results [4][5][6][7] since it was born. Catastrophe theory analyzes complicated system, builds catastrophe model.…”

Minimal Model for Sprag-Slip Oscillation as Catastrophe-Type Behavior

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Stability Analysis of Rectangular Plate Based on Catastrophe Theory

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