Equilibrium of a Radially Symmetric Inhomogeneous Plate Under Tension and Load

This paper studies a mathematical model for small deflections of a radially symmetric strongly inhomogeneous elastic plate under a normal load and tension in the center plane. The type of inhomogeneity studied occurs in injection molded plastics. The model consists of a Dirichlet boundary value problem for a linear fourth-order ordinary differential equation. A general expression is derived for physically reasonable solutions under relatively broad restrictions on the inhomogeneity and load. The solutions are analyzed and interpreted in terms of their physical significance.