Layup optimization for buckling of laminated composite shells with restricted layer angles

The layup optimization for maximizing buckling loads of long laminated composite cylindrical shells subjected to combinations of axial compression, external lateral pressure, and torsion is carried out on the basis of Flugge's theory. The layer angles, that is, fiber orientation angles, of the laminated composite cylindrical shells are restricted to the values of 0, 45, -45, and 90 deg, and then nine lamination parameters are used as design variables for the layup optimization. Explicit expressions relating the nine lamination parameters are derived and used to describe the feasible region in the design space of lamination parameters. Thus, the layup optimization problem becomes a constrained nonlinear optimization problem, and the optimum lamination parameters are determined by a mathematical programming method. The laminate configurations aiming to realize the optimum lamination parameters are obtained by analytic formulas or by an unconstrained optimization procedure. It is observed that, for the laminated composite cylindrical shells with the layer angles restricted to the values of 0, 45, -45, and 90 deg, the optimum buckling loads are less than 10% lower than the optimum buckling loads obtained for unrestricted laminate configurations.