Application of Lagrange multiplier method to rectangular all-edge clamped plates

An analytical form of a solution to the boundary-value problem of thin all-edge clamped rectangular plates of an isotropic material subjected to a uniform gravity loading is presented. A generalized solution technique developed by Kabir and Chaudhuri (1992) is further advanced to a thin plate boundary-value problem to solve three highly coupled second-order partial differential equations with constant coefficients resulting from the application of the First Order Shear Deformation Theory. The solution functions are selected in such a way that they satisfy the clamped boundary conditions in a manner similar to the Navier method. The Lagrange Multiplier Method is applied to the First Order Shear Deformation-based formulation for all-edge clamped boundary conditions in obtaining a thin plate response. The numerical results presented include deflection and bending moment characteristics, and variations of these quantities with respect to various aspect ratios. The numerical results obtained from the present study are compared with the available classical thin plate results, First Order Shear Deformation Theory-based analytical and finite element results. The limitations of the Lagrange Multiplier Method to the present application are also discussed.