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

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.