Small and large deformation models of post-buckled beams under lateral constraints

Abstract

This study aims at theoretically and experimentally investigating the buckling behavior of bilaterally constrained beams with respect to different geometric parameters and conditions. The theoretical models are developed based on small and large deformation theories, respectively. The nonlinear Euler–Bernoulli beam theory is used to form the governing equations. An energy method is introduced to solve the equilibrium beams by minimizing the total potential energy with respect to the weight coefficients of the buckling modes. The theoretical models are compared with experiments. Good agreements are obtained with respect to the force–displacement relationship and deformed beam shape configuration. This study indicates that the small deformation model is insufficient in predicting beam end shortening since the longitudinal displacement is negligible in the model. The large deformation model effectively predicts severe deflection of beams in terms of end shortening and rotation. Parametric studies are carried out to indicate the applicability of the presented models. In particular, the small deformation model is defined as “more applicable” when the difference of the post-buckling response between the small and large deformation models is less than 5% (Diff < 5%), given that its computational cost is generally smaller than the large model. In contrast, when the difference is greater than 5%, the large deformation model is suggested. In the end, a polynomial function is fitted to define the relationship between the ratio of net gap-to-beam length η and highest achievable buckling mode Φ. The presented small and large deformation models are effective in understanding and predicting the post-buckling responses of laterally confined beams under different conditions.