КРУГЛІ ПЛИТИ НА ПРУЖНІЙ ОСНОВІ ЗІ ЗМІННИМ КОЕФІЦІЄНТОМ ПОСТЕЛІ

Abstract

The paper considers the application of the analytical method - the method of direct integration - to the calculation of building structures in the form of round and annular plates and slabs lying on a continuous variable elastic basis. The application of the proposed approach allowed to obtain solutions of a wide class of problems, the mathematical summary of which are differential equations with variable coefficients or systems of such equations, and at the same time to evaluate the possibilities and accuracy of calculation of finite elements. The base reaction is described by the Winkler model with a variable bed ratio. With respect to the bending of round and annular plates, formulas for the function of deflections and its derivatives, transverse force and bending moments are obtained. The method is applicable under any given boundary conditions on the contours. The calculation is reduced to determining from the given boundary conditions of the unknown constants of integration and numerical realization of the obtained solutions. The found formulas of the general form are transformed for practically important case when the factor of a bed and loading have the form of polynomials. It is shown that in this case dimensionless fundamental functions are represented by static series. To calculate the coefficients of static series, the corresponding recurrent relations are derived. The calculations show that the discrepancy in the results of the calculation of the deflections of the FEA and the author’s method (AM) is insignificant (not more than 1%), and the results of the calculation of radial and circumferential moments differ significantly, and this difference sometimes reaches 12-14%. However, when the grid is condensed in the circumferential direction, the picture changes, there is a convergence of the results obtained by two methods. This indicates the inaccuracy of the finite element analysis performed on the basis of automatic partitioning of the finite element grid. And this, in turn, leads to "blind" reinforcement of reinforced concrete slabs, in which it is possible, both re-reinforcement of the structure and its insufficient reinforcement.