Post-buckling analysis of compressed rods in cylinders by using dynamic relaxation method

Buckling of rods with cylindrical constraints is an essential problem in engineering and medical fields. Completely different to the buckling of classical Euler rods, the post-buckling modes for rods with cylindrical constraints involve highly complicated deformations and geometric configurations. In this paper, the rods are discretized into beam elements by finite element method, and the constraint relation between the rods and cylinders is described by gap element. A dynamic relaxation method for static buckling of compressed rods in cylinders is introduced. Numerical simulations have been carried out to investigate the effects of damping, element length, initial contact stiffness and penetration on post-buckling, etc. The characteristic buckling modes include deflection curves with single point, two points, three points and point-line-point contact. For the helical buckling, it is found that the transition section consists of two noncontact sections only, while the perturbed-helix section does not exist. Except the critical load and shear force of helical buckling, numerical simulation results are in good agreement with the analytical solution. By using the dynamic relaxation method, stable helical buckling modes can be obtained directly without undergoing sinusoidal buckling deformation under given compressive loads.