Cord-reinforced cylindrical shells

Methods for determining the load-deformation behavior of cord-reinforced cylindrical shells are developed. A cord-reinforced composite consists of cords embedded in a matrix. These composites are unique in that the cords have extension-twist coupling. Current uses of cord-reinforced composites include pneumatic tires, air springs, hoses, flexible couplings, belts, bladders, flexible diaphragms, and various membrane structures. The most common application of a cord-reinforced shell is the automobile or truck steel-belted radial tire, where steel cords are embedded in a rubber matrix. The objective is to develop the tools to assess the effects of changes in the geometry and/or constituents of a cord-composite shell on the load-deformation behavior.; In this work, an analytical approach is used to develop the equations for the displacements from the loads on a cord-reinforced cylindrical shell. The load-deformation relations are developed by considering the mechanics of the matrix, the cords, and the shell. The matrix is modeled using the generalized Hooke's law for an isotropic linear-elastic material. The theory that is used to model the cords was developed by Costello and includes the extension-twist coupling of the cords. For the shell, a set of differential equations for the displacements is derived based upon the analysis of the bending of circular cylindrical shells by Flugge, an equilibrium approach. These equations are solved analytically in closed form for axisymmetric loading. The resulting load--deformation relations are strongly dependent upon the properties of the constituents, including the extension-twist coupling of the cords, and the geometry, boundary conditions, and loading of the cord-reinforced cylindrical shell.