Anisotropic thin-walled beam models: a rational deduction from three-dimensional elasticity

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.