In this paper anisotropic thin-walled beam models are rationally deduced from
three-dimensional elasticity by means of a constrained approach. Consistent
frictionless internal constraints on both stress and strain dual fields are enforced
through a modified Hu–Washizu functional obtained by a nonstandard application of
Lagrange multipliers. Beam theories accounting for different shear refinement levels
are justified, showing that this variational approach enables the development of new
refined models, including high-order nonconventional effects and enhancing standard
treatments of shear deformation effects. In agreement with the constrained problem,
a locally equilibrated approximation of the stress field acting on beam cross-section is
recovered in closed form. Finally, cases of laminated thin-walled beams as well as of
unilateral conewise constitutive behavior (with special reference to bimodular
materials) are investigated.
