Determination of Deflections of the Plates under Localized Loads

We consider the problem of evaluation of displacements in plates subjected to the action of localized loads by using the relations of the theory of elasticity and applied theories. The solution of the problem in the presencce of forces is obtained with the help of the Lurie symbolic method and the Vashchenko-Zakharchenko expansion formulas in the form of exponential series. To find the displacements near the sites of application of the forces, where the constructed series are slowly convergent, we additionally use the Hankel integral transformation. We propose a procedure for the selection of slowly decaying components of the integrands, which can be used to represent the displacements in terms of rapidly convergent Taylor series. The cases in which the applied theories can be used for finding deflections are specified.