Analysis of laminated circular cylinders of materials with the most general form of cylindrical anisotropy.: II. Flexural deformations

This second paper of a two-part series is devoted to flexural stresses and deformations in a laminated anisotropic cylinder of perfectly bonded materials possessing the most general form of cylindrical anisotropy. The loading conditions include pure bending, flexure by a transverse force, and applied surface tractions that lead to resultant transverse loads and bending moments of uniform or linear variation along the axis. These loading conditions cause strain and stress fields that are uniform, linear and quadratically varying along the axis. The solutions herein are based on the relaxed formulation of the Saint-Venantʹs and Almansi–Michell problems where conditions on the ends of the cylinder are satisfied on an integral basis rather than on a point-wise basis. Differences in the stress distributions between these integral conditions with any point-wise specification are self-equilibrated states that decay with distance into the interior, i.e., Saint-Venantʹs principle. Means to account for such effects are discussed.