An enhanced Hencky bar-chain model for bending, buckling and vibration analyses of Reddy beams

Abstract

This paper is concerned with the development of the so-called Hencky bar-chain model for the bending, buckling, and vibration analyses of non-uniform thick beams. The conventional Hencky bar chain model comprises a finite number of rigid segments connected by frictionless hinges and elastic rotational springs and lumped masses at the joints. The key contribution of this paper is to enhance the Hencky bar chain model for the analysis of thick beams through the adoption of a third-order shear deformable (or Reddy) beam theory to allow for the effect of transverse shear deformation. The paper also shows the validity of the analogies between the enhanced Hencky bar-chain model and the central finite difference method for solving partial differential equation systems that have been observed for the Euler-Bernoulli beam model.