Numerical approximation of the classical solutions for plates

Resumo

This article proposes a solution, obtained by line adjustment, to the problem of bending of thin plates
with small deflections. The aim of this solution is to make the programming and manual calculation of bending
moments and deflections easier than classical method equations and calculation tables. The values to make the fit
was obtained by programing the Levy’s classical method in MATLAB® and the results were close to the values
given by Timoshenko e Goodier (1959). The line adjustment was made in MATLAB® and the shape function was
a polynomial equation of third degree with four variables. Furthermore, the values obtained numerically was
compared with the coefficients in Chust and Figueiredo’s (2014) calculations table. It was verified that the
tabulated values were not the maximums because they were always obtained in the middle of the plate. Therefore,
a new calculation table for each kind of plate with the maximum values is proposed along with closed form
approximations. The analyses were carried out for rectangular plates with clamped or simply supported edges.