A GENERALIZED FORMULATION FOR RADIALLY GRADED COMPOSITE CYLINDERS/ RINGS WITH MAXIMIZED BUCKLING STABILITY LIMITS

This paper presents a generalized formulation for the problem of maximization of buckling stability limits of anisotropic, functionally graded, thin-walled rings/long cylindrical shells subjected to external pressure. The main structure was built of laminated composites having different volume fractions of the constituent materials within the individual plies. This yield to a piecewise grading of the material in the radial direction; that is the physical and mechanical properties of the composite material are allowed to vary radially. The objective function was measured by maximizing the critical buckling pressure while preserving the total structural mass at a constant value equals to that of a baseline reference design. In the selection of the significant optimization variables, the fiber volume fractions adjoined the fiber orientation angles and plies thicknesses. The mathematical formulation employed the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately as well as the inclusion of the coupling stiffness terms was presented. The proposed model deals with dimensionless quantities in order to be valid for thin shells having arbitrary thickness-to-radius ratios. The critical buckling pressure level curves augmented with the mass equality constraint were given for several types of anisotropic rings/long cylinders showing the functional dependence of the constrained objective function on the selected design variables. It was concluded that material grading have a significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.