Post-buckling of thin-walled aeronautical structures induces failure modes related to skin-stiffener separation that require three-dimensional large deformation analyses for an accurate numerical prediction. Conventional finite elements are capable of solving such analyses, but with high associated computational costs, being therefore more utilized for the simulation of smaller structural components, or even restricted to perform virtual testing at coupon-level models. In this paper, a geometrically nonlinear reduced-order method using a hybrid-stress solid-shell formulation is proposed for large deformation analysis of thin-walled structures. Current reduced-order methods are mainly applicable to buckling problems, considering only the out-of-plane deformation. Furthermore, existing displacement-based reduced models involve a computationally expensive fourth-order tensor obtained with the higher-order strain energy variations. Here, a reduced-order model with only one degree of freedom is constructed for both in-plane and out-of-plane large deformation problems. It is shown that, with the hybrid-stress formulation, the constructional efficiency of the reduced system is largely improved by zeroing the fourth-order strain energy variation using the two-field Hellinger–Reissner variational principle, followed by a condensation of the stress terms that lead to a third-order approximation of the equilibrium equation. The nonlinear predictor solved by the reduced-order model can be corrected when its numerical accuracy is not satisfactory during the path-following analysis. A simple plate, a honeycomb cell with negative Poisson ratio, and a swept-back wing structure; are used as numerical examples to verify that the proposed method enables a superior path-following capability for the three-dimensional analysis of thin-walled structures undergoing large deflection, large rotation and large strains. Furthermore, an experimental validation of the proposed method is presented using a variable-thickness plate with mixed composite-metallic materials, undergoing large out-of-plane deflection.

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.