Reliability Based Design Optimization (RBDO) of Randomly Imperfect Thin Cylindrical Shells Against Post-Critical Drop: Fid-Bau Portal

Reliability Based Design Optimization (RBDO) of Randomly Imperfect Thin Cylindrical Shells Against Post-Critical Drop

Majumder, Rohan / Mishra, Sudib K.

Thin cylindrical shells have wide applications owing to its large specific bending stiffness as well as very light weight design. Buckling of shells in the elastic regime is a critical consideration in design. The Knock Down Factors (KDFs) are specified for designing against the significant disparity between the analytical (linearized) critical load with the experimental, obtained as a product of the linearized critical load and the KDFs. The closely spaced buckling modes undergoes nonlinear interactions amongst themselves which is the main reason behind such reductions. In addition, it is also triggered by the presence of inherent imperfections. However, the KDFs are largely over-conservative, as they are estimated as the lower bounds of the experimental data set. These margins can be narrowed down by non-linear analysis, accounting for the random imperfections. Hence, the present study re-evaluates the KDFs to achieve a target reliability through RBDO. The prohibitively exhaustive computations in RBDO are by passed by proposing a Power law Meta-Model akin to the Koiter’s law of imperfection sensitivity. The power law meta-model is in contrast to the conventional polynomial meta-models often employed in reliability analysis. Further, the stochastic sensitivity of the KDFs (w.r.t the design variables) are equated for optimality and simplifications. The proposed approach is shown to offer significant accuracy and computational efficiency, as demonstrated on a thin cylindrical shell with random imperfections, modelled by a zero-mean, Stationary, Gaussian Stochastic field with appropriate auto-correlations. The static Riks method is conveniently used for the nonlinear finite element (FE) analysis of the shell buckling/post-buckling employing the commercial code ABAQUS. The permissible imperfections for obtaining a particular reliability index using a specific KDF are presented, which may be useful for probabilistic quality control in the construction/fabrication of cylindrical shells.