Novel two-level strategy to exactly solve multilayer composite cantilever tubes of cylindrically orthotropic materials

Abstract

A novel two-level strategy is employed to solve the multilayer composite cantilever tubes in elasticity theory. On the first level of our strategy, a complete stress field is developed for the inclined winding cantilever tubes. Thus the tube can be considered as a bending-like tube including the proportional moments together with a shear-like tube including the constant shear forces. The pure bending formula is used to obtain the solution for the bending-like tube. However, the shear-like tube includes some additional terms from the bending-like tube. Therefore, on the second level of our strategy, the shear-like tube is broken into two independent systems according to whether the additional terms are included. Thus their different circumferential functions can be satisfactorily separated from the radial functions. In addition, an approach of undetermined coefficients is employed to find the particular solution for the second independent system. In the examples the method in this paper is used to exactly solve the composite cantilever tubes [90°], [45°] and [75°] as well as [45°/75°], [75°/−75°] and [(75°/−75°)40]. The good agreement of our exact results with the numerical simulation with fine finite elements shows the accuracy and effectiveness of the method in this paper.