The Koiter-Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced-order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton-Raphson method using the full model. In this paper, we proposed a modified Newton-type KN method to trace the geometrically nonlinear response of structures. The developed predictor-corrector strategy is applied to each predicted solution of the reduced-order model. The reduced-order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced-order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced-order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.

Efficient bolted joint design is an essential part of designing the minimum weight aerospace structures, since structural failures usually occur at connections and interface. A comprehensive numerical study of three-dimensional (3D) stress variations is prohibitively expensive for a large-scale structure where hundreds of bolts can be present. In this work, the hybrid composite-to-metal bolted connections used in the upper stage of European Ariane 5ME rocket are analyzed using the global-local finite element (FE) approach which involves an approximate analysis of the whole structure followed by a detailed analysis of a significantly smaller region of interest. We calculate the Tsai-Wu failure index and the margin of safety using the stresses obtained from ABAQUS. We find that the composite part of a hybrid bolted connection is prone to failure compared to the metal part. We determine the bolt preload based on the clamp-up load calculated using a maximum preload to make the composite part safe. We conclude that the unsuitable bolt preload may cause the failure of the composite part due to the high stress concentration in the vicinity of the bolt. The global-local analysis provides an efficient computational tool for enhancing 3D stress analysis in the highly loaded region.