A geometrically nonlinear reduced-order method using hybrid-stress solid-shell formulations for 3D large deformation analysis of thin-walled structures

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.