A rational deduction of plate theories from the three-dimensional linear elasticity

In this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three-dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu-Washizu functional, governing the constrained elasticity problems. Both the first-order shear deformation plate theory, and the higher-order Lo-Christensen-Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.