Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 2. Calculation Results for Continuous Circular Plates

Continuous circular plates on a variable elastic foundation are considered. It is assumed that the reaction of the foundation is described by the Winkler model with the variable modulus of subgrade reaction, defined as a polynomial. We present in the analytical form all required computational formulas, which make it possible to conduct axisymmetric bending tests of continuous circular plates on a continuously variable elastic foundation with a variable continuously distributed load, specified by a polynomial. Examples of the calculation of plates are presented. Two possible cases of boundary conditions are considered: hinging and fixing along the plate contour. A calculation of plates acted upon by a constant load is performed by a method developed by the authors, with a modulus of subgrade reaction varying linearly and parabolically. To verity the results obtained, a modeling and calculation of the same plates is performed via a software package implementing the finite element method. Comparison of the results obtained proves the feasibility of the proposed algorithm, which requires no structural discretization. Due to analytical solutions obtained, the calculation accuracy is improved. The method provides a more reliable results on bending of plates relative to approximate methods. Therefore, it is a good alternative to approximate methods in the axisymmetric bending analysis of continuous circular plates on a variable elastic bed.