Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion

Exact solutions of elastic Kirchhoff plates are available only for spe- cial geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint- Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one con- tributed in (Acta Mech, 224(12), 2955-2964 (2013)) for the special case of homoge- neous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided