Effect of radial reaction force on the bending of circular plates resting on a ring support

In the classical analysis of bending of a circular plate resting on simple support when subjected to transverse loading, the effect of the radial component of the reaction force is often neglected. This paper analyzes the effect of the radial component of the reaction force on the bending of thin circular plates using the Kirchhoff plate theory. A nonclassical axisymmetric bending problem is studied. By solving the governing equation based on linearization of nonlinear theory of elasticity, two typical cases including uniformly distributed loading over a plate surface and a concentrated force at the plate center are considered. Expressions for the large- and small-scale deflection and rotation are obtained and a non-linear load-deflection relation is given. When neglecting the radial reaction force, a linearized model is reduced and its solution coincides with that of classical thin circular plates. The deflection and load-deflection response curve are graphically presented for centrally-loaded and uniformly-loaded circular plates, respectively. A comparison of the deflections with and without the radial reaction force is made. Obtained results are useful in safety design of linear and non-linear plates under complicated loading.