Rational derivation of a single-layer model for laminated thin-walled beams

In this paper an equivalent single-layer theory for the analysis of laminated thin-walled beams is rationally deduced from the three-dimensional elasticity theory. Consistent constraints for strain and stress fields are enforced in the Hu-Washizu functional by a non-standard application of the Lagrange multipliers theory. Vlasov-Wagner assumptions on the middle-surface of the beam and Kirchhoff-Love restrictions are enforced as strain constraints together with dual conditions on the constitutive-related stress field. The linearly elastic properties of the equivalent single-layer beam are deduced considering an anisotropic constitutive behaviour for each lamina. The proposed model takes into account high-order effects related to thickness and curvature of the cross-section centerline, usually neglected, allowing to deduce a refined expression of the torsional warping function for open cross-section laminated beams.