A generalized model for heterogeneous and anisotropic beams including section distortions

• The beam model takes into account non-uniform warpings and section distortions.
• It is obtained through a Ritz–Galerkin approximation using independent descriptions of the stress and displacement fields.
• They are evaluated by a semi-analytic solution based on a finite element description of the cross section.
• The model includes the generalized Saint Venànt solution for heterogeneous and anisotropic materials.
• A mixed finite element has been used to validate the beam model.

A linear model for beams with compact or thin-walled sections and heterogeneous anisotropic materials is presented. It is obtained by means of a Ritz–Galerkin approximation using independent descriptions of the stress and displacement fields. These are evaluated by a preliminary semi-analytic solution based on a finite element description of the cross section. A coherent definition of the deformations and stresses is obtained which includes both the generalized Saint Venànt solution for generic materials and some significant additional effects, due to out-of-plane warping and section distortions. The so-built 1-D model maintains the richness of the 3-D solution using a small number of variables.