On the boundary conditions for a thin circular plate conjugated to a massive body

Abstract

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.