Closed form solutions of axisymmetric bending of circular plates having non-linear variable thickness

A new analytical method for evaluation of elastic stresses and deformations in axisymmetric plates having variable thickness according to a power of a linear function, either solid or annular, subjected to symmetrical bending due to lateral loads either distributed on upper surface or distributed along the inner or the outer edges. The proposed procedure is based on two independent integrals of the hypergeometric differential equation describing the rotation field and constitutes the generalization of the one found in the literature. This method allows to study a wide range of plates, be they solid or annular, converging or diverging with linear or non-linear thickness function, convex, concave or linear tapered, without the restrictions of the known procedures. Analytical results obtained by using this method utterly match both theoretical results which may be obtained in the specific case known (constant-thickness circular plate, linear variable thickness annular circular plate) and numerical results obtained by using FEA.