A novel and highly efficient strategy to determine the ‘Worst’ imperfection shape for buckling of cylindrical shell panels

Abstract

The cylindrical shell panels subjected to in-plane compression experience more complex snap-back behavior associated with sharp turning around the limit-point load. The initial geometric imperfections play a significant role in the evaluation of the limit load along the nonlinear buckling response. Due to the highly computational cost for imperfection sensitivity analyses, the determination of a ‘worst’ imperfect shape that leads to the minimum limit load becomes a challenge. In this work, the initial geometrical imperfection shape is assumed to be the combination of numbers of closely-spaced buckling modes with different participation coefficients. The reduced order model based on the improved Koiter theory is constructed using all the closely-spaced modes, only once for ‘perfect’ structure and then applicable for any imperfections by just updating the independent imperfection term. Independent imperfection terms with gradient and Hessian forms are designed to be suitable for imperfections with small and relatively large magnitudes, respectively. The optimization strategy is developed to find out the optimal participation coefficients of closely-spaced modes that give the ‘worst’ imperfect shape. Two imperfection sensitivity indices, the limit load under a certain imperfection magnitude and the reduction factor of limit load under a certain interval of imperfection magnitudes, are defined and applied as the objective functions, respectively. The genetic algorithm is selected to find the optimal solutions efficiently benefiting from the a posteriori accounts of imperfections in function calls. Cylindrical shell panels with various configurations are applied to validate the good performance of the proposed strategy.