Deformation of a Thin Circular Plate Fixed along the Contour to the Substrate

In the approximation of the Foppl-von Karman model, the problem of deformation of a circular plate coupled to a massive substrate along a contour coinciding with the boundary of a hole in the substrate under the action of a transverse load is solved. Boundary conditions of two types were considered: rigid and generalized elastic embedding. The solution is obtained in two ways: by decomposing into power series the transverse displacements and longitudinal forces represented in a cylindrical coordinate system, as well as by numerical integration of the Foppl-von Karman equations, with successive refinement of boundary conditions, similar to the “shooting method”. Expressions for the displacement components of a circular plate are obtained. The role played by the compliance of the substrate in changing the profile shape of the circular plate, the acting longitudinal forces and bending moments has been revealed. A comparison with other solutions has been made. The fields of applicability of the methods are investigated.