Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure

This paper presents a mathematical model for enhancing the buckling stability of composite, thin-walled rings/long cylinders under external pressure using radial material grading concept. The main structure to be analyzed is built of multi-angle fibrous laminated lay-ups having different volume fractions of the constituent materials within the individual plies. This leads to a piecewise grading of the material in the radial direction. The objective is to maximize the critical buckling pressure while preserving the total structural mass at a constant value equal to that of a baseline design. The fiber volume fractions are included among the standard design variables such as fiber orientation angles and ply thicknesses, which are used by many investigators in the field. The model employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately is given. The critical buckling pressure contours subject to the mass equality constraint are given for several types of anisotropic rings/long cylinders showing the functional dependence of the constrained objective function on the selected design variables. It is shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.