Nonlinear Modal Responses of Damaged Shell Structures: Numerical Prediction and Experimental Validation

Abstract

The nonlinear finite element (FE) modeling approach has been adopted to model and predict the modal responses of the combined damaged (crack and delamination) layered shell structures. The damaged panel structure has been constructed mathematically using a circular meshing approach of the FE technique to include the crack. Similarly, the sublaminate approach has being used to introduce delamination of the layered structure on a mutual center. The structural distorted geometry and the deformations were modeled through the full geometrical nonlinear strain-displacement (Green–Lagrange) relations in association with higher-order polynomial functions. The modal responses of the damaged structure were obtained through an iterative method in association with the nonlinear FE technique. The predicted response accuracies were established with two-step verifications: that is, the numerical solution stability (elemental sensitivity) and the degree of deviation with published data. The maximum deviation between the developed numerical model and the reference result (first-order shear deformation theory) was 8.3%. The model’s competence and responses were compared with experimental data, with and without damages. Finally, new examples have been solved for different structural geometry-dependent parameters (shell configurations, delamination shapes, crack positions/lengths, end boundaries, etcetera) affecting final modal values. A detailed in-depth understanding of the damage and curvature (unequal/equal curvature) effects on modal responses will be discussed.