A BEAM THEORY CONSIDERING CROSS-SECTIONAL DEFORMATION DUE TO THE POISSON EFFECT

Abstract

Since, in homogeneous beams, the displacement perpendicular to the axis by the Poisson’s effect is not constrained, elementary beam theory uses a one-dimensional elastic constitutive law. However, in composite beams consisting of multiple materials with different Poisson’s ratios, the multiple materials constrain each other’s displacement in the perpendicular direction to the axis. Since the axial stiffness and the bending stiffness are affected by this displacement constraints, accurate evaluation of the stiffness needs to consider the Poisson’s effect. In this paper, we propose a beam theory that can consider Poisson’s effect as an extension of the beam theory including the cross-sectional deformation. Comparison of the solutions of the proposed beam and continuum shows the validity of the proposed beam theory.