A new approach to elastic branching analysis

Abstract

A new perturbation approach to the analysis of elastic post-buckling and imperfection sensitivity of discrete structural systems is presented. This approach by-passes the lowest branching point and obtains estimates of the post-buckling response of the perfect system and the imperfection-sensitivity of imperfect systems by equilibrium projections at constant load from the fundamental equilibrium path, this being possible when the response of imperfect systems is related to a dominant post-buckling path of the perfect system. The new scheme is conceptually simpler than the conventional perturbation approach (which makes projections from the lowest critical equilibrium state of the perfect system), and in addition it overcomes an inherent weakness of the conventional approach which arises when energy coefficients vary rapidly with the load or when there are neighbouring critical equilibrium states on the fundamental equilibrium path close to the one under consideration. It should be particularly effective when the dominant post-buckling path lies close to the fundamental path. A feature of the new approach is that while it can be used as a powerful ad hoc method in regions remote from the lowest critical point it nevertheless retains the essential characteristics of a branching theory able to resolve fine details in the vicinity of a critical equilibrium state. In the presence of a dominant post-buckling path the method can be used in the presence of discrete, simultaneous and near-simultaneous critical points, being particularly useful in the latter case when conventional approaches may experience difficulties. The new approach is applied to the analysis of the imperfection-sensitivity of a buckling model exhibiting an asymmetric point of bifurcation and to the post-buckling analysis of an Euler strut, these studies confirming the promise of the approach.