An asymptotic linear thin-walled rod model coupling twist and bending

Abstract

A linear one-dimensional model for thin-walled rods with open strongly curved cross-section, obtained by asymptotic methods is presented. A dimensional analysis of the linear three-dimensional equilibrium equations yields dimensionless numbers that reflect the geometry of the structure and the level of applied forces. For a given force level, the order of magnitude of the displacements and the corresponding one-dimensional model are deduced by asymptotic expansions. In the case of low force levels, we obtain a one-dimensional model whose kinematics, traction, and twist equations correspond to the Vlassov ones. However, this model couples twist and bending effects in the bending equations, unlike the Vlassov model where the twist angle and the bending displacement are uncoupled