Analogies between Kirchhoff plates and Saint-Venant beams under flexure

New exact solutions for isotropic Kirchhoff plates, with no kinematic boundary constraints, are inferred by an analogy with the cross-section warping of orthotropic, homogeneous Saint-Venant beams bent and twisted by a shear force. The procedure is based on a formal equivalence between the elastic equilibrium conditions, respectively, for the tangential stresses in terms of a warping function in a Saint-Venant beam and for the bending-twisting moment in a Kirchhoff plate. The analysis refers to simply or multiply connected plates with an isotropic elastic stiffness proportional to the beams warping function. The result extends the one provided by the author for the special case of simple torsion (Barretta, Acta Mech 224(12):2955-2964, 2013). An example for a circular plate is developed, thus providing a new benchmark for computational mechanics.