An analytical solution to the problem of interaction of a circular plate with an inhomogeneous soft layer

We consider axisymmetric problem of theory of elasticity i.e. bending of a plate lying on an inhomogeneous foundation. The foundation is modeled by an elastic inhomogeneous soft interlayer and an elastic homogeneous half-space. The interlayer can be stratified or continuously inhomogeneous with arbitrary varying elastic properties and can be significantly softer than the underlying half-space. The plate is bent under the action of distributed load and elastic response from the foundation. Analytical solution of the problem is constructed using coupled asymptotic method (Aizikovich, 1990). Analytical expressions for contact stresses and deflections of the plate are provided. Constructed solution is asymptotically exact both for large and small values of the geometric parameter of the problem (ratio of a layer thickness to the plate radius). Also it is applicable both for flexible and stiff plates. Numerical results provided for different types of variation of elastic properties in the interlayer are compared with the results obtained by other methods.