On the general contact problem of an inflated nonlinear plane membrane

The nonaxisymmetric contact problem between an inflated membrane and a rigid indentor is considered. The membrane is assumed to be an initially thin plane sheet. The shape and the boundary of the contact region and the configuration of the deformed membrane under both inflation and indentation are found by employing the minimum potential energy principle subjected to an inequality constraint condition. A slack variable that converts the inequality constraint to an equality constraint condition is introduced. The coordinate functions that describe the deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy are determined by Fletcher and Powell's1] iterative descent method for finding the minimum of a function of multivariables.