Hencky bar-chain model for buckling and vibration of beams with elastically restrained ends

This paper presents the Hencky bar-chain model for buckling and vibration analyses of beams with elastically restrained ends. The Hencky bar-chain model is composed of rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The key contribution of this paper lies in the modelling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first order central finite difference beam model. The establishment of such a physical discrete beam model allows one to obtain accurate solutions for beam like structure with repetitive cells (or elements).