We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height ε. We then study, by means of Γ-convergence, the asymptotic behavior as ε goes to zero of the sequence of complementary energies. The limit functional is then identified as a dual problem for a two-dimensional plate. Our approach gives a direct characterization of the convergence of the equilibrating stress fields. This paper has been published in Math. Mech. Solids, 23, (2018), pp. 1119-1139, doi 10.1177/1081286517707998