Abstract
The present paper deals with the instabilities of a bending tube. When an increasingly large amount of bending moment is applied to the ends of a circular tube, ovalization occurs at its cross-section before it finally buckles. This ovalization is referred to as the Brazier effect and the result of which is the decrease in the tube's geometrical stiffness. After buckling, the tube collapses with a local kink in the longitudinal direction. The tube responses described above are, in this paper, investigated with a nonlinear finite element method that uses the hyperelastic shell model. By conducting numerical analysis, we detect the bifurcation paths,trace the post-buckling equilibrium paths and depict the corresponding buckled configurations.From the numerical analyses, it is revealed that there are two critical points, a bifurcation point and a limit or turning point, before the limit point that Brazier estimated. Symmetrical kinks are observed along the primary path as final largely deformed configuration, while only one kink along the furcation path. In the both cases, the deformation suddenly jumps to the kink mode at the same rotation angle. The numerical results demonstrate the ability of presented approach and examine the bending instabilities of a tube.
