INVESTIGATING BUCKLING OF FUNCTIONALLY GRADED SANDWICH NANO-BEAMS WITH HIGHER ORDER SHEAR DEFORMATION THEORY

Abstract

The present research focuses on the analysis of buckling in FGM beams, incorporating a non-local theory and Poisson's effect within its analytical framework. A higher-order transverse shear field has been employed, utilizing a novel warping shape function. The equilibrium equations have been derived analytically from energy principles, with the numerical solution of these equations based on energy minimisation using the Ritz method. A comparative study was conducted to explore the variation of the dimensionless critical buckling with respect to different higher-order deformation theories. This study utilised a simply supported FGM (metal-ceramic) beam, excluding Poisson's effect, to analyse the influence of various parameters. A secondary application was performed on a sandwich beam, incorporating nonlocal theory and Poisson's effect, to investigate the effects of different beam slenderness ratios and variations in volume fraction index. The results of the dimensionless critical buckling analysis demonstrated that the Poisson effect significantly influenced the behaviour of the system. Furthermore, it was observed that the nonlocal effect behaves in a distinct manner depending on the beam slenderness, a phenomenon attributable to its interconnection with shear effects, which are more pronounced in short beams.