Rotational Spring Analogy for Buckling Analysis

Abstract

This paper presents a “rotational spring” analogy which allows the geometric stiffness for a large class of structural problems to be formulated using common notions from linear structural analysis. The proposed analogy offers an intuitive framework which (1) sheds significant light on geometric nonlinearity in general, and buckling analysis in particular; (2) explains previous buckling analysis procedures, and (3) is directly applicable to the simplified buckling analysis of discrete as well as continuum structures. This paper discusses the application of the proposed analogy to single degree-of-freedom, multidegree-of-freedom, as well as continuous structural systems, providing in the process several illustrative examples. These demonstrate the simplified framework offered by the proposed rotational spring analogy for a wide range of buckling problems, and highlight its conceptual power in furthering the understanding of important issues in geometrically nonlinear analysis.