Nonclassical axisymmetric bending of circular Mindlin plates with radial force

Abstract

The classical analysis of bending of a circular plate subjected to transverse loading often neglects the effect of the radial component of the reaction force. This paper analyzes this effect for a moderately thick circular plate with roller constraint. A nonclassical axisymmetric bending problem of a circular Mindlin plate is studied for a concentrated force and uniformly distributed loading. The governing equation is derived based on the incremental deformation theory of elasticity. With the aid of Bessel functions, explicit expressions for small- and large-scale transverse deflections and section rotation are obtained. Singular behavior at the plate center is discussed in detail. Two possible hypotheses at the plate center are analyzed, and they give rise to different singularities of the deflection, rotation, and stresses at the plate center. When neglecting the radial reaction force component, our model reduces to the classical circular Mindlin plate theory. Obtained results are useful in the safety design of circular plates under complicated loading.