Efficient buckling analysis and optimization method for rotationally periodic stiffened shells accelerated by Bloch wave method

Abstract

Rotationally periodic stiffened shells have been widely used as load-bearing parts in engineering structures, however, the buckling analysis and optimization of stiffened shells suffer from large computational time owing to the large-scale and complex development tendency of engineering structures. Considering that most of the traditional equivalent buckling analysis methods do not retain the features of stiffeners and cannot capture local buckling, their prediction accuracies in buckling load and mode are not high enough although they can reduce the analysis cost. In this paper, an efficient buckling analysis and optimization method is proposed for rotationally periodic stiffened shells accelerated by Bloch wave method. Firstly, the derivation of Bloch wave boundary conditions for buckling analysis of the substructure is presented, along with the corresponding numerical implementation procedure. Based on the buckling analysis method accelerated by Bloch wave method, the Kriging-based Efficient Global Optimization method is used to improve the optimization efficiency. Then, typical examples are carried out for the buckling analyses of stiffened cylindrical shells with various grid patterns including orthogonal grids, triangle grids, rotated triangle grids, mixed triangle grids and hierarchical orthogonal grids, as well as the integrally stiffened shell with non-straight generatrix. Compared with buckling results from the direct finite element analysis, the proposed method achieves high prediction accuracy in buckling load and remarkable improvement in modelling and analysis efficiency simultaneously. Particularly, the proposed method succeeds in capturing both local buckling mode and global buckling mode. Finally, the optimization design of the integrally stiffened shell with non-straight generatrix is carried out based on the proposed method aiming at maximizing the buckling load. Results indicate that the proposed method can reduce the total optimization time significantly and improve the buckling load by 94.5%, contributing to providing meaningful references for the design large-scale engineering structures.