A Higher Order Theory Applied to Beams Resting on Elastic Foundations

The mixed variational principle of Reissner (1950) was used here to derive higher order equations for beams. The stress and displacement states of the classical theory were modified to include two higher order effects (this was called the third order theory). These stress and displacement states were used in the variational principle. The governing equations and boundary conditions appeared in such a form that the symmetric and antisymmetric parts were uncoupled and hence could be considered separately.