Free vibration analysis of corrugated panels using homogenization methods and a cell-based smoothed Mindlin plate element (CS-MIN3)

The behavior analysis of complex structures like corrugated panels usually requires high-cost shell modeling which is an obstacle in subsequent studies such as parametric study and optimization. To overcome the difficulty, many homogenization models in which equivalent orthotropic plates replaces the original shells have been proposed. However, there is a lack of investigations for verifying their accuracy and reliability. In this paper, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) is integrated with typical homogenization models to give some homogenization methods for free vibration analyses of trapezoidally and sinusoidally corrugated panels. Using the results of ANSYS and ABAQUS shell simulations as references, the accuracy and reliability of the homogenization methods are illustrated through several numerical examples. The influences of geometric parameters such as the number of corrugation units, corrugation amplitude, trough angle, and panel thickness are studied and some important remarks about the performances of these methods are derived.