The effect of Poisson's ratio on the stiffness properties of composite beams

Abstract

We investigate whether the stiffness of a non-uniform beam of a coaxial structure made of isotropic materials can be calculated using engineering (Bernoulli-Euler) theory. We derive a condition necessary and sufficient for the coincidence of the stiffnesses predicted by the asymptotic and the engineering theories. It turns out that this condition involves the Poisson's ratio, only. If the derived condition is not satisfied, the stiffnesses of the inhomogeneous beam always exceed those predicted by engineering theory. In other words, the engineering stiffnesses are exact low boundaries for the actual stiffnesses of a beam.Our numerical calculations verify our theoretical conclusions, and demonstrate that the difference in the mentioned stiffnesses can be very large.