On the Reissner theory of bending of elastic plates (Q1084929)

The Reissner equations of elastic plates are rederived on the basis of the incomplete generalized variational principle of complementary energy. The stress function \(\psi\) is naturally obtained from the variational calculation with Lagrange multipliers. The structure of solutions of the Reissner equations is thus defined. On the basis of these discussions, a simplified theory has been put forward, in which the equations of equilibrium involving the shearing influence can be reduced to a fourth order differential equation similar to those of the classical theory of plates.