Analysis of laminated circular cylinders of materials with the most general form of cylindrical anisotropy.: I. Axially symmetric deformations

A procedure is presented for the analysis of stresses and deformations in a laminated circular cylinder of perfectly bonded materials with the most general form of cylindrical anisotropy. Attention is focused in this paper on axisymmetric loads, and a companion paper will be devoted to loads producing flexural deformations. Axisymmetric loading conditions include an axial force and torque on the ends as well as a general distribution of surface tractions of pressure, circumferential shear and longitudinal shear. These surface tractions are represented by a power series in the axial coordinate. Only the leading two terms are considered herein; they relate to uniform and linear variations of the normal pressures and uniform circumferential and longitudinal surface shears. From the methodology for these two terms, extension of the analysis procedure for higher terms will be readily apparent. The solutions herein fit descriptions of (1) the relaxed formulation of Saint-Venantʹs problem where prescribed tractions on the ends on a point-wise basis are replaced by integral conditions relating to an axial force and torque and (2) the Almansi–Michell problem. Differences in the stress distributions between these integral conditions with any point-wise specification are self-equilibrated states that evanesce with distance from the ends, i.e., Saint-Venantʹs principle, and some remarks are offered for treatment of such effects.