Finite Grid Analogy for Levy Plates on Generalized Foundations

In many engineering problems the need for accurate and rapid computation of stresses and deformations in Levy plates on 2-parameter foundations is encountered. The challenge may be met in a simplified way by resorting to a finite grid model of intersecting beams on generalized elastic foundations. The simplified formulation in this article is based on the discretized representation for plates composed of interlocking girders endowed with exact stiffness, geometric stiffness, and consistent mass matrices. These have been obtained through the use of exact shape functions. Sample problems of bending, buckling, and free vibration problems for rectangular Levy plates supported on elastic foundations are solved. Comparisons with known analytical solutions and other numerical solutions are presented.