Buckling Analysis of the Discrete Planar Cosserat Rod

In this paper, a discrete model of the planar Cosserat rod is presented. Based on the calculus of variations, the equilibrium equations of the model are derived for potential forces and hyperelastic material. Buckling of the structure under axial loading is thoroughly studied assuming linear elasticity. Dimensionless stiffness parameters are introduced, and analytical solutions are given for the critical loads and the corresponding buckled shapes of the model. Classification of the axially loaded structure is accomplished based on the number, sign, and physical admissibility of its buckling loads. It is revealed that the model can possess several buckling modes under tension.