Large deformation solutions to post-buckled beams confined by movable and flexible constraints: A static and dynamic analysis

Abstract

This paper develops a static and dynamic large deformation model to investigate the post-buckling response of slender beams constrained by movable and flexible bilateral confinements. A novel discretization algorithm is proposed to convert the irregular constraints into gap vectors. Governing equations are formulated based on the Euler-Bernoulli beam theory. An energy method is presented to solve the equations using a modified Nelder–Mead algorithm. A constrained minimization of the total energy is carried out with respect to the gap vectors. The theoretical results of the proposed model, i.e., the deformed beam shape configuration and force-displacement relationship, are compared with existing studies and experiments. The regularly and movably constrained, static model is compared with the existing small and large deformation models, respectively. The regularly and flexibly confined, dynamic model is compared with experiments. Satisfactory agreements are observed. Parametric studies are conducted to investigate the post-buckling response in terms of loading and constraints conditions. In particular, the loading condition is first examined by changing the loading frequency. The highest achievable buckling mode is then studied with respect to the Young's moduli ratios of movable constraints-to-beam and flexible constraints-to-beam, respectively, and the ratio of walls gap-to-beam length. The proposed theoretical models are effective in understanding and predicting the static and dynamic post-buckling response of beams constrained by movable and flexible confinements.