Series-Based Solution for Analysis of Simply Supported Rectangular Thin Plate with Internal Rigid Supports

In this study, Navier's solution for the analysis of simply supported rectangular plates is extended to consider rigid internal supports. The proposed method offers a more accurate solution for the bending moment at the critical section and therefore serves as a better analytical solution for design purposes. To model the plate-support interaction, the patched areas representing the contact between the plate and supports are divided into groups of cells. The unknown internal reactions at the centers of the divided cells are obtained by satisfying the compatibility conditions at the centers of the cells. Three numerical examples are presented to demonstrate the accuracy of the proposed analytical solution. The given examples reveal good agreements with those obtained by the finite element analysis. In addition, they show the advantage of the new solution as compared to the existing analytical solution which inaccurately estimates the location and magnitude of the maximum bending moment.

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