Asymptotic derivation of a general linear model for thin-walled elastic rods

Abstract

In this work we derive from three-dimensional elasticity a general mathematically justified theory for thin-walled elastic rods. This theory is obtained as an asymptotic approximation of the three-dimensional linear model as the area and the thickness of the cross-section becomes successively small. It constitutes an extension of the classical Vlassov's theory for thin-walled beams (the most complete among models currently used in engineering).