The Inflation and Contact Constraint of a Rectangular Mooney Membrane

Abstract

This paper presents a minimum energy solution for the deformed configuration of an edge-bonded rectangular membrane loaded with uniform pressure and contacting a frictionless rigid constraint. A technique borrowed from optimization theory is employed to derive a potential energy functional which contains the contact constraint condition with no increase in the number of independent functions. This energy functional is minimized by a series of geometrically admissible, continuous, coordinate functions with constant coefficients determined by the Ritz procedure. The variable-metric method, as generalized by Fletcher and Powell, is used to find the coefficients in the energy minimizing series solutions. The results presented show the contact boundary and the distortion of a square gridwork laid on the undeformed membrane.