Design and optimization of laminated conical shells for buckling

Optimum laminate configuration for the maximum buckling load of filament-wound laminated conical shells is investigated. In the case of a laminated conical shell, the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and the weight of the structure. Thus, optimization can be performed by maximization of the buckling load for a specific weight, or by minimization of the weight of the structure under the constraint of applied buckling load. Due to the complex nature of the problem a preliminary investigation is made into the characteristic behavior of the buckling load with respect to the volume as a function of the ply orientation.The exact buckling load is calculated by means of the computer code STAGS-A (Structural Analysis of General Shells [Almroth BO, Brogan FA, Meller E, Zele F, Petersen HT. Collapse analysis for shells of general shape, user's manual for STAGS-A computer code. Technical report AFFDL TR-71-8; 1973]) by adding a user written subroutine WALL, see Ref. [Goldfeld Y, Arbocz J. Buckling of laminated conical shells taking into account the variations of the stiffness coefficients. AIAA J 2004; 42(3):642–649]. The optimization problem is solved using response surface methodology.