Axisymmetric Bending of Circular Plates on a Variable Elastic Base

An algorithm of direct integration method for calculation of annular plates lying on elastic Winkler base with variable bedding coefficient under the action of transverse load is proposed. To verify the results obtained by the proposed method, the finite element method implemented in PC LIRA-SAPR is used. Two examples of calculations are considered. Analysis of the results shows that the values of deflections practically coincide in calculations of a circular plate by the author's method and by the finite-element method, and discrepancy between the values of bending moments reaches 9.3 %. Moreover, the discrepancy in deflections appears only in the fourth (and sometimes even in the fifth) decimal place. It is noted that the method of direct integration has demonstrated very high accuracy in solving numerous problems of deformable solid mechanics that have exact solutions. The discrepancy in the values of bending moments obtained here is related to the semi-automatic breakdown of the finite-element mesh in PC LIRA-SAPR. This statement is based on the fact that when the mesh is thickened in the circumferential direction, the results obtained by the two methods in determining the radial and circumferential bending moments converge considerably.