CALCULATION OF ANNULAR PLATES ON AN ELASTIC BASE WITH A VARIABLE BEDDING FACTOR

Abstract

The application of the analytical method ‒ the method of direct integration ‒ to calculations of building structures in the form of circular plates and plates on a continuous variable elastic base is considered. It is noted that there are no proposals for a general analytical method for calculation of annular plates on a variable elastic base in the literature. And the need for such a method is obvious, since it makes it possible to estimate the accuracy of finite element analysis. A detailed description of the algorithm of the direct integration method is not given in the paper, and all the calculation formulas for the circular plate are taken from the authors’ already published article. The results of numerical implementation of this algorithm for specific examples are considered. In order to verify the results of calculations by the author’s method, computer modeling of the considered circular plates in PC LIRA-SAPR and their calculations by the finite element method have been performed. The reaction of the foundation is described by the Winkler model with a variable bedding factor. The calculation of a concrete slab that is rigidly pinched on the inner contour and articulated on the outer contour is performed. And calculation of a steel plate with rigid pinching on the outer contour and articulated on the inner contour. In the first case, the bedding factor is assumed constant, and in the second case, it changes according to the linear law. The calculations showed that the discrepancy between deflections calculated by the finite-element method and the author’s method does not exceed 1%, and the results of radial and circumferential moments calculation differ more considerably, amounting to 10%. The authors explain this difference by the inaccuracy of the numerical analysis associated with a semi-automatic method of constructing a finite-element mesh, which should be made finer. The densification of the mesh in the manual mode of its partitioning significantly reduces the discrepancy between the results of calculating the deflections, radial and circumferential bending moments by the finite-element method and the author’s method.