Mechanics of a Near Net-Shape Stress-Coated Membrane. Volume I of II: theory Development Using the Method of Asymptotic Expansions

摘要

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.