An Analytical Model for Nonlinear Static and Buckling Analysis of Sandwich Auxetic Cylinders with Functionally Graded Face Sheets Under Combined Axial and Radial Loading

This study presents an analytical formulation for evaluating the nonlinear equilibrium equations and axial buckling behavior of functionally graded (FG) auxetic cylinders subjected to combined axial and radial loading. The FG auxetic cylinder includes two inner and outer FG layers and one re-entrant honeycomb core layer. The mechanical properties of the FG layers vary through the thickness, and the presented formulation applies to any FG layers with power-law volume fractions. The governing equations are derived using the first-order shear deformation theory (FSDT) and von Kármán nonlinear relations. Nonlinear equilibrium equations are solved using the perturbation technique, while a closed-form solution is obtained for the stability equations with variable coefficients. A detailed parametric study explores the effects of FG layer properties, geometric features, and re-entrant honeycomb core parameters on both deformation and buckling performance. Results show that FG layers significantly impact the structural response. Radial displacement is highly sensitive to radial loading, and positive radial pressure improves buckling resistance. The influence of honeycomb geometry is limited. These insights offer valuable guidance for the optimal design of FG auxetic cylinders in structural and multifunctional applications.