Bending of a Partially Supported Circular Plate

Abstract

We consider the problem of bending of a thin circular plate under the action of concentrated normal forces at its center in the case where the plate rests on two symmetrically located contour supports of finite length. The integral equation of a Prandtl-type problem is numerically solved by the method of mechanical quadratures and the method of orthogonal polynomials. Moreover, it is reduced to the Fredholm integral equation of the second kind. We compute the distribution of generalized shear forces in the support and the deflection of the plate.