On the issue of calculating a rigid rectangular isotropic plate with a rigidly fixed contour under the action of a concentrated load in the center of the plate

The article considers the issue of the correctness of the calculation of the bending of a rectangular rigid isotropic plate with a clamped perimeter under the action of a centrally applied concentrated force. It is shown that various sources devoted to the analysis of this calculation scheme offer different formulas for determining the maximum deflection at the plate center and the maximum value of the specific bending moment at the center of the long edge of the plate. Moreover, conventionally, the reference literature offers two types of calculation formulas for determining each of these quantities. A search has been conducted for various works and articles devoted to the issue considered in the article. Several sources have been found in which the sequence of solving the bending of these plates can be disclosed in detail, but these sources are deposited. An analysis of the dimensions of the calculation formulas and auxiliary calculation coefficients has been performed. Calculations have been performed for three different plates with a change in the aspect ratio. The correct calculation formula is selected based on a comparative analysis of the calculation results with the calculation of plates by the finite element method in the Fidesys software package. Within the framework of the considered calculation schemes, the error in determining the maximum deflection and the maximum value of the specific bending moment along the long side of the plate according to one group of formulas does not exceed 5 %, while according to another group of formulas, the calculation error reaches 75 %. The error in applying the calculation formulas for plate materials with a Poisson's ratio different from 0.3 has been determined.

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