A natural perturbation method with symmetric secant stiffness for stability analyses of quasi-perfect thin-walled structures

With the advance of manufacturing techniques, quasi-perfect thin-walled structures with initial geometrical imperfections are widely used in engineering. However, much experience is needed to introduce proper perturbations to consider the impact of these undetermined imperfections on structural stability. In this paper, a symmetric secant stiffness method considering the accumulated stress gradients is established through energy approach. With this approximation of the exact stiffness matrix, natural perturbations can be introduced into stability analyses. Numerical examples and experimental comparisons demonstrate that the proposed method can obtain reasonable results for quasi-perfect thin-walled structures merely based on perfect geometrical models. •A natural perturbation method is proposed for structural stability analyses.•A symmetric secant stiffness matrix is constructed from the stress gradients.•The method can indicate if the structure is sensitive to imperfections.•The influence of unknown inevitably small imperfections can be naturally considered.