A useful solution for estimating contact pressure between a plate and foundation

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 trample is a blank holder (plate) pressed again st 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 variabl es are typically the thickness and modulus of the plate, the stiffness of t he foundation and the applied pressure distribution on the noncontacting si de of the plate. In general the problem relating the variables to the conta ct pressure distribution is three-dimensional and requires a complex finite element or boundary element solution. However, if the applied pressure dis tribution consists of sufficiently localized parches, which is often the ca se in applications, then an approximate 3D solution can be constructed by s uperposition. Specifically, the paper provides a convenient calculation pro cedure for the contact pressure due to a single circular parch of applied p ressure on an infinite, isotropic, elastic layer which rests on a Winkler f oundation. The procedure is validated by using known analytical solutions a nd the finite element method (FEM). Next a sensitivity study is presented f or ascertaining the validity of the solution's use in constructing solution s to practical problems involving multiple patches of lending. This is acco mplished through a parametric study of the effects of loading radius, laver thickness, layer elastic properties, foundation stiffness and the form of the applied pressure distribution on the magnitude and extent of the contac t pressure distribution. Finally, a procedure for determining an appropriat e Winkler stiffness parameter for a foundation is presented. [S1087-1357(00 )00603-1].