ON A MIXED VARIATIONAL THEOREM AND ON SHEAR DEFORMABLE PLATE-THEORY

We first complement a recent formulation of a variational equation for displacements and some stresses in infinitesimal elasticity. We now derive an analogous result from a statement of the general variational equation for displacements and all stresses. In the second part of this paper we use the results of the first part for the derivation of an approximate tenth-order linear theory of bending and stretching of anisotropic nonhomogeneous plates. The advantage of the present derivation depends on the fact that use of the variational equation for displacements and some stresses allows, in a natural way, for a treatment of the stresses which will be continuous in the direction of the plate thickness in a manner which differs from the treatment of those stresses which may be discontinuous, as a consequence of material property discontinuities.