АППРОКСИМАЦИЯ ПРОГИБОВ ПЛАСТИНОК, ЛЕЖАЩИХ НА ВИНКЛЕРОВОМ ОСНОВАНИИ

Abstract

The purpose of this research is to develop the method of shape factor interpolation for calculating the maximum deflection of thin plates on an elastic Winkler base, which are widely used in modeling the operation of elements of building constructions of buildings and structures. The above calculation method allows to obtain solutions based on direct analytical dependences, the argument of which is an integral characteristic of a flat convex one-connected area - the shape factor. This characteristic has applications in a number of problems of mathematical physics and is known from the works of scientists G. Polia and G. Szegö. The shape factor was first applied to the calculation of plates by Professor V.I. Korobko. The method of interpolation by shape factor was developed by Professor A.V. Korobko. When determining the maximum deflection of thin plates on an elastic base, some parameters of the problem are considered as functions of the shape factor of the plate in consideration and are determined by the type of boundary conditions on its contour. The present study is devoted to the construction of approximating functions for continuous sets of plates of characteristic outlines and boundary conditions. The paper presents functions for calculating the maximum deflection of elastic plates in the form of isosceles triangles, rhombuses and rectangles. The plates with various combinations of hinged support and rigid pinch along their individual sides, loaded with a continuous uniformly distributed load, are considered. The established functional dependences are intended for direct use in the calculation of plates of the specified outlines, as well as for obtaining reference solutions during interpolation of the values of maximum deflections of plates of more complex outlines.