A RATIONAL DEDUCTION OF PLATE THEORIES FROM THE 3-DIMENSIONAL LINEAR ELASTICITY

In this paper a general procedure for a rational derivation of plate t heories is proposed. The methodology is based on the conjecture that p late 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 variati onal principles, based on the Hu-Washizu functional, governing the con strained elasticity problems. Both Me first-order shear deformation pl ate theory, and the higher-order Lo-Christensen- Wu plate theory are d erived. The governing equations are recovered, and Me reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium: c ongruence: and constitutive equations turn out to be exactly satisfied .