On the Reissner theory of bending of flastic plates

Abstract

The Reissner equations of elastic plates are rederived on the bases of the incomplete generalized variational principle of Complementary energy. The Stress function ψ is naturally obtained from the variational Calculation in the form of Lagrange multiplier. The stucture of solutions of the Reissner equations is thus defined. On the bases of these discussions, a simplified theory has been put forward, in which the equations of equilibrium involving the shearing influence can be reduced into a fourth order differential equation similar to those of the Classical theory of plates.