A mixed beam model with non-uniform warpings derived from the Saint Venànt rod

• The beam model takes into account the non-uniform warping effects due to shear and torsion.
• The model is generated through a mixed formulation with an independent description of displacement and stress fields.
• Two different descriptions for the stress field are proposed and tested.
• The model exactly contains the classical Saint Venànt solution.
• A mixed finite element based on exact shape functions has been used to validate the beam model.

A new linear model for beams with compact or thin-walled section is presented. The formulation is based on the Hellinger–Reissner principle with independent descriptions of the stress and displacement fields. The kinematics is constituted by a rigid section motion and non uniform out-of-plane warpings related to shear and torsion. The stress field is built on the basis of the Saint-Venànt (SV) solution and with a new part to describe the variable warping.The formulation of a finite element with exact shape functions made possible to validate the beam model avoiding discretization errors.