Approximate solution for the compression buckling of fully anisotropic cylindrical shells

The circular cylindrical thin-walled shell is a fundamental building block of many structures, such as aircraft fuselages. When used with laminated composites, highly efficient structures can be designed. As a result, the analytical treatment of cylindrical shells has received significant attention over recent decades. However, most of the works carried out in this area concern isotropic materials or orthotropic laminates, that is, those with no couplings. The present analysis develops a closed-form, yet simple solution for the linear buckling of laminated circular cylindrical shell, from the Donnell's model, including all available couplings. Although the usefulness of a linear solution for predicting buckling loads is questionable, its worth is in initial sizing and layup selection during the early stages of design. The resulting model could be used to examine the usefulness of different couplings that are not yet well understood. It is found that extension/shear coupling results in torsional movement of the cylinder, which, when restricted, induces a secondary torsional loading on the cylinder, thus reducing its overall buckling load by up to 50%. When not restricted, extension/shear couplings generally increase buckling loads.