Examples of exact solutions for problems of bending plate with free face planes

The paper discusses examples of exact solutions of the boundary problem on the bending of a thin elastic semi-infinite plate, in which the long sides are free, and at the end are self-balanced bending moment and generalized shear force are specified. The solutions are obtained in the form of the series in Papkovich–Fadle eigenfunctions. The unknown expansions coefficients are determined by formulas and are expressed via the Fourier integrals of the boundary functions specified at the plate side.