Axisymmetric bending of circular sandwich plate on elastic foundation with complicated structure

The approximate closed-form solution to the problem on a circular multilayer (sandwich) constant-thickness plate bending on an elastic foundation with a complicated structure is obtained. The plate is bent under the axisymmetric distributed load, and the foundation reaction. The elastic foundation is a uniformly irregular in thickness layer (coating) based on a homogeneous half-space (substrate). Young’s modulus value at the interface of the coating and the substrate has a significant leap. Two different cases of the boundary conditions are considered for the plate: fixed and free edge conditions. The constructed approximate analytical solution to the problem is effective for a wide range of both geometric (the inhomogeneous layer thickness and the plate radius) and physical parameters (plate flexibility, and elastic properties of the coating and the substrate). The contact problem is reduced to the system of the integro-differential equation solution through the integral transformation method. The obtained formulas can be used for calculating the contact interaction characteristics between a multilayer plate and a foundation with a complex structure in various cases of the boundary conditions, and various loads applied to the plate.