Proper-Orthogonal-Decomposition-Based Buckling Analysis and Optimization of Hybrid Fiber Composite Shells

Composite cylindrical shells have been widely used in the fuel tanks of launch vehicles. To reduce the material cost of carbon-fiber-reinforced polymer shells, hybrid fiber composite shells composed of carbon fibers, glass fibers, and an epoxy matrix would be a more promising choice. Along with the development of heavy lift launch vehicles, the diameter of a required shell structure could become large. The buckling analysis of composite shells based on detailed finite element models was too time consuming. From the point of view of model size reduction, accurate reduced-order models for buckling analysis along with optimization methods were needed to improve the efficiency of the design and analysis cycle of composite shells. A combined proper orthogonal decomposition and optimization method is proposed in this paper for an efficient buckling analysis of composite shells. In the offline steps of proper orthogonal decomposition, one single finite-element-model buckling analysis is performed based on a full-order model of the initial design with the certain volume fractions of hybrid fibers. Furthermore, snapshots generated from the eigenvector values of the finite-element-model buckling analysis result from the initial design, and a proper orthogonal decomposition basis is determined. By using the obtained proper orthogonal decomposition basis from the initial design, the online steps of proper orthogonal decomposition can be carried out for the buckling analysis of any composite shell with varying volume fractions of hybrid fibers. To further improve the prediction accuracy for a large design space, the mixed proper orthogonal decomposition snapshot method is proposed by adding additional proper orthogonal decomposition snapshots into the original ones. The proposed method contributes to improving the prediction accuracy among the entire design space significantly. Finally, a low-cost optimization framework is established for hybrid fiber composite shells, during which the proper orthogonal decomposition method is used for accelerating the buckling analysis. In particular, a convergence criterion and an updated proper orthogonal decomposition basis strategy are proposed for the optimization framework, aiming at guaranteeing the credibility of the optimal proper orthogonal decomposition buckling result. By means of an illustrative example, the effectiveness and efficiency of the developed framework are demonstrated.