Mechanics of a near Net-Shape Stress-Coated Membrane : Theory Development Using the Method of Asymptotic Expansions

The method of asymptotic expansions was applied to the geometrically nonlinear, three-dimensional equations of a coated membrane laminate, each material component of which was assumed to be a linear, uniform, homogeneous, and isotropic elastic material in which there exist residual stresses. Our goal was to systematically derive by a single method the generalizations of four well-known theories of a single material to a coated membrane laminate. Two of the theories, one geometrically linear, the other geometrically nonlinear, describe a true membrane laminate offering no resistance to bending. These are applicable to membrane laminate vibration analysis, and pressurized stress- coated membranes undergoing large deflections, respectively. The other two describe stress-coated membrane shells having small but non-zero bending stiffness; these theories are to be used to determine a coating stress prescription that will maintain the shape of an initially parabolic stress- coated membrane laminate. Solutions of associated boundary value problems are given in Volume II of the report.Air Force Research Lab Kirtland Afb Nmdirected Energy Directorate is the author of 'Mechanics of a near Net-Shape Stress-Coated Membrane : Theory Development Using the Method of Asymptotic Expansions', published 2002 under ISBN 9781423548188 and ISBN 1423548183.