Nonlinear Vibration Correlation and Buckling Analysis of Flat Plates and Shells

The employment of nondestructive techniques in aerospace industries is rising thanks to advances in technologies and analysis. This part of the aerospace testing industry is essential to design and validate the new structures’ methodology and safety. Therefore, robust and reliable nondestructive methods have been extensively studied for decades in order to reduce safety problems and maintenance cost. One of the most important and employed nondestructive methods to compute large-scale aerospace structures’ critical buckling load is the Vibration Correlation Technique (VCT). This methodology allows to obtain the buckling load and equivalent boundary conditions by interpolating the natural frequencies of the structures for progressively increasing loadings without considering instabilities. VCT has been successfully investigated and employed for many structures, but it is still under development for composite shell structures. The present work provides a numerical model for carrying out virtual VCT to predict the buckling load, to characterize the natural frequencies variation with progressive higher loadings, and to provide an efficient means for verifying the experimental VCT results. The proposed nonlinear methodology is based on the well-established Carrera Unified Formulation (CUF). CUF represents a hierarchical formulation in which the structural model’s order is considered the analysis’s input. According to CUF, any theory is degenerated into generalized kinematics and is compactly handled. By adopting this formulation, the nonlinear governing equations and the relative FE arrays of the two-dimensional (2D) theories are written in terms of Fundamental Nuclei (FNs). FNs represent the basic building blocks of the proposed formulation. In order to investigate far nonlinear regimes, the full Green-Lagrange strain tensor is considered. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. For an assessment of the robustness of the virtual VCT, several flat plate and shell structures are studied and compared with the solutions found in the available VCT literature. The results prove that the proposed approach provides results with an excellent correlation with the experimental ones, allowing to investigate the buckling load and the natural frequencies variation in the nonlinear regime with high reliability.