A Naghdi-type linear model for rods with little regularity

In this paper, we rigorously analyse a linear elastic isotropic rod model of the Naghdi type. The model is formulated in the functional space H 1 , without additional constraints in the function space and well defined for W 1 , ∞ parametrisation of the middle line. We prove the model’s mathematical well-posedness. The model is justified through a detailed asymptotic analysis, showing that its solution converges to the same limit as the solution of the three-dimensional (3D) equations of linearised elasticity as the thickness parameter ( h ) tends to zero. The proposed model is compared, both analytically and numerically, against the flexural rod model and the full 3D elasticity equations.