Buckling of Three‐Dimensional Rigid‐Link Models

Abstract

Two‐dimensional rigid‐link models have been used often in the study of elastic stability to provide insight into the behavior of engineering structures; the buckling modes of such models take only planar shapes. Many engineering structures, however, possess three‐dimensional buckling characteristics, so it is important to have models with three‐dimensional buckling characteristics. A three‐dimensional three‐link model that initially assumes either a straight‐line or a planar zigzag configuration is studied and both in‐plane and out‐of‐plane buckling modes are found in each case. The model is formulated in terms of the total potential energy and differentiation is carried out using the MACSYMA program. This structure may deflect continuously with increasing load, buckle in a plane, or buckle out of plane, depending on the angle between the adjoining links and the relative stiffness between the bending springs and the internal rotation springs. We find that in the case of in‐plane buckling, the buckling load is greater than the lowest buckling load of the perfect structure.