Analogies between Kirchhoff plates and Saint-Venant beams under torsion

Torsion of linearly elastic homogeneous and orthotropic Saint-Venant beams is based on the solution of a Neumann-like boundary value problem for the cross-sectional warping. Equivalence of differential conditions of elastic equilibrium for the beam twist stresses in terms of warping function and for the bending-twisting moments in a Kirchhoff plate is assessed. The analogy provides new exact solutions in the theory of thin plates. Examples are developed for composite plates with no kinematic boundary constraints. Elliptic and equilateral triangle shapes provide useful benchmarks for computational mechanics.