Self-buckling with initial imperfections: Application to trees

Abstract

In most structural systems, initial imperfections, such as initial deflection, is an unavoidable challenge, and it significantly influences buckling. This study aimed to theoretically explain the effect of initial deflection and initial slope on self-buckling characteristics of heavy columns subjected to self-weight. Specifically, we examined cantilevers composed of isotropic material with a constant cross-section. Accounting for both self-weight and axial compression load, we developed a formula characterizing the self-buckling problem for some simplified cases such as sin-curve, hypergeometric curve, and straight line (initial slope). Consequently, we established the relationship between the self-buckling characteristics and the level of initial imperfections. We discovered that the greatest height for self-weight buckling is proportional to the 2/3 power of radius, regardless of the initial imperfection. Moreover, our findings suggest the potential to predict the height of tree-like natural structures using the greatest height formula and considering initial imperfections.