A Useful Solution for Estimating Contact Pressure Between a Plate and Foundation

Abstract

Many manufacturing situations involve a finite thickness plate or layer of material which is pressed against a much thicker foundation of the same or different material. One key example is a blank holder (plate) pressed against a die (foundation) in a sheet metal forming operation. In designing such a plate/foundation system the design objective often involves the contact stress distribution between the plate and foundation and the design variables are typically the thickness and modulus of the plate, the stiffness of the foundation and the applied pressure distribution on the noncontacting side of the plate. In general the problem relating the variables to the contact pressure distribution is three-dimensional and requires a complex finite element or boundary element solution. However, if the applied pressure distribution consists of sufficiently localized patches, which is often the case in applications, then an approximate 3D solution can be constructed by superposition. Specifically, the paper provides a convenient calculation procedure for the contact pressure due to a single circular patch of applied pressure on an infinite, isotropic, elastic layer which rests on a Winkler foundation. The procedure is validated by using known analytical solutions and the finite element method (FEM). Next a sensitivity study is presented for ascertaining the validity of the solution’s use in constructing solutions to practical problems involving multiple patches of loading. This is accomplished through a parametric study of the effects of loading radius, layer thickness, layer elastic properties, foundation stiffness and the form of the applied pressure distribution on the magnitude and extent of the contact pressure distribution. Finally, a procedure for determining an appropriate Winkler stiffness parameter for a foundation is presented. [S1087-1357(00)00603-1]