In this paper, we rigorously analyse a linear elastic isotropic rod model of the Naghdi type. The model is formulated in the functional space , without additional constraints in the function space and well defined for 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.
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