Optimal laminate configurations of cylindrical shells for axial buckling

Optimum laminate configurations for laminated cylindrical shells under axial compression are investigated and obtained under buckling constraints. Complete freedom is given in the selection of the ply angle variation through the thickness. Twelve lamination parameters are introduced to describe laminate properties, and the optimal values of these parameters are obtained numerically. It is shown that there are many different optimal configurations which give the same buckling load. The optimality condition for the laminate configurations is derived semiempirically from the numerical results in terms of the lamination parameters. The maximum buckling load is obtained in terms of material properties. Some examples of optimal laminate configurations are presented. It is shown that one of the optimal laminate configurations can be obtained when an infinite number of infinitely thin layers are arranged so that the shell becomes quasi-isotropic in the shell surface and quasihomogeneous through the thickness.