Buckling and vibration of Hencky bar-chain with internal elastic springs

H. Zhang (1) , C. M. Wang , Noel Challamel (2)

1 NUS - National University of Singapore
2 IRDL - Institut de Recherche Dupuy de Lôme

This paper presents the Hencky bar-chain model (HBM) that allows for the presence of internal elastic springs. With the development of this general HBM, one can analyse beam-like structures with repetitive cells with allowance for internal damaged sections or bracing members. In this paper, we have derived formulas for the internal rotational and lateral spring stiffnesses of HBMs based on the finite difference model (FDM). In addition, the analytical buckling loads and vibration frequencies of the HBM and FDM with internal elastic springs are presented for the first time. These analytical solutions converge to the exact solutions for continuum beams when the HBM segmental number approaches infinity. The solutions can also be used to calibrate the Eringen's small length scale coefficient e(0) in the nonlocal beam theory based on their phenomenological similarities.

Mots clés: Buckling; Vibration; Hencky bar-chain; Central finite difference; Internal elastic spring stiffness; Exact solution

Domaines: Matériaux

H. Zhang, C. M. Wang, Noel Challamel. Buckling and vibration of Hencky bar-chain with internal elastic springs. International Journal of Mechanical Sciences, 2016, 119, pp.383-395. ⟨10.1016/j.ijmecsci.2016.10.031⟩. ⟨hal-02110744⟩