Summation rules in critical self-buckling states of cylinders

Abstract

This study aimed to derive a critical height formula that would be uniformly applicable to hollow and solid cylinders, to clarify the effects of hollow cross-sections on self-buckling characteristics. The models used for our calculations took the cylindrical cantilevers with cavities of arbitrary radius. The governing equation was obtained from the equilibrium of forces. The eigenvalue problem obtained by applying appropriate boundary conditions to the general solution of the governing equation led to the derivation of a critical height formula. Furthermore, based on the derived theoretical formula, we found that the self-weight buckling properties of a hollow cylinder could be represented as a summation of the self-weight buckling properties of two solid cylinders, which can be derived more easily. The findings of this study have a wide range of applications, such as the simplification of complex buckling problems and the shape quantification of hollow plants.