A finite grid solution for circular plates on elastic foundations

The transmission of vertical or horizontal structural forces to the supporting soil is a challenge to analyze for structures on elastic foundation which represent a complex medium. The two-parameter elastic foundation model that provides a mechanical interaction between the individual spring elements shows a more realistic behavior of the soil reaction than does the single parameter Winkler model. Since the structural behavior of a beam resembles that of a strip in a plate, in this study, the exact stiffness and mass matrices of the beam element on two-parameter elastic foundation is extended to plates. The framework method that replaces a continuous surface by an idealized discrete system can represent a two-dimensional plate. In the light of this situation, circular plates are modeled as an assemblage of individual beam elements interconnected at their neighboring joints in radial and tangential direction. So, a useful tool called finite grid solution as a numerical method developed in this study lead to solve circular plates resting on two parameter elastic foundation problems. Examples for bending of ring, circular and annual plates on elastic foundation are solved to compare with known analytical solutions and other numerical solutions. The comparisons show that the literature and the computed results are compatible.