A limit-based approach to the stress analysis of cylindrically orthotropic composite cylinders (0/90) subjected to pure bending

Composite cylinders are used in many engineering applications. Solution for a single orthotropic cylinder subjected to bending load was provided by Lekhnitskii [1]. Solution for composite cylinders made of many layers subjected to pure bending has been provided by Jolicoeur and Cardou [4]. However these methods do not provide systematic solution for the cases where the layers are oriented at 0° or 90° with respect to the cylinder axis. The reason is that the number of available equations is fewer than the unknowns due to the fact that some of the equations simplify down to identities. Thus the unique solution cannot be obtained. In order to overcome this problem, a limit-based approach is presented in this paper, where the limit to the cylindrical orthotropy is considered, and by using the Taylor series of expansion, the equations replacing the identically satisfied ones are derived. It is also found that this method is a generalization of the L'Hopital's Rule to the case of multi-unknowns with multi-equations, some of which are identically satisfied. In the numerical examples, the results by the proposed approach are compared with those obtained from NASTRAN. It is found that they are in good agreement to each other.