Abstract
For thin elastic plates of arbitrary shape with a smooth pinched or hinged contour based on the modified Rayleigh-Ritz method, explicit expressions are obtained for the approximate values of the maximum deflection from a uniformly distributed load, the deflection at the point of application of the concentrated force, the critical force of uniform compression, and the first eigenfrequency. The lateral movements were approximated by special functions having level lines similar to the plate contour. The results of calculating the plate in the form of a pear-shaped oval are presented, which are in good agreement with the two-sided geometric estimates of the corresponding solutions
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