Generalized Variational Principle of Plates on Elastic Foundation

The theory of variational principle is enhanced by using the Lagrange multiplier to establish a generalized variational principle for plates on an elastic foundation. In the first part of this paper, the principle of minimum potential energy is introduced in which the integral equation is employed as the variational constrained condition. In the second part, it is shown that the generalized variational principle with two variational functions can be established. This represents, to the authors’ knowledge, the first treatment of the variational principle with these types of equations.