The use of nondestructive techniques in the aerospace industry 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 costs.One of the most important and employed nondestructive methods to compute the critical buckling load of large-scale aerospace structures is represented by the Vibration Correlation Technique (VCT).&nbsp;This method allows to obtain buckling loads and equivalent boundary conditions by interpolating the natural frequencies of the structures for progressively increasing loadings without reaching the instability point. It has been successfully investigated and employed for many structures, but it is still under development for thin-walled composite shells.In this context, the present work provides a numerical model for carrying out virtual VCT, to predict the buckling load, to characterize the variation of the natural frequencies with progressive higher applied load, and to provide an efficient means for the verification of the experimental VCT results.In order to obtain accurate results as in the experimental test, the proposed nonlinear approach is formulated in the framework of the well-established Carrera Unified Formulation (CUF). CUF represents a hierarchical formulation in which the order of the structural model is considered as an input of the analysis. Thus, no ad-hoc formulations are needed to achieve any refined generic model.&nbsp;According to CUF, any theory is degenerated into generalized kinematics adopting an arbitrary expansion of the generalized variables. With this procedure, the nonlinear governing equations and the relative FE arrays of the two-dimensional (2D)&nbsp;theories are formulated in terms of Fundamental Nuclei (FNs). FNs are the basic building blocks of the proposed formulation. The full Green-Lagrange strain tensor is employed because far nonlinear regimes are investigated. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method along with a path-following approach based on the arc-length constraint.For a robustness assessment of the virtual Vibration Correlation Technique, different flat plate and shell structures&nbsp;are studied and compared with results found in the available VCT literature. The results demonstrate that the proposed approach provides results with a very good correlation with the experimental ones, allowing to predict the buckling load and the variation of the natural frequencies in the nonlinear regime with high reliability.

Nonlinear Vibration Correlation and Buckling Analysis of Flat Plates and Shells

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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