Postbuckling Analysis of Functionally Graded Beams Using Nonlinear Model

Abstract

The major novelty of the paper in the study, post-buckling of simply supported FGM beams using various theory, classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), parabolic shear deformation beam theory (PSDBT) and exponential shear deformation beam theory (ESDBT). Governing equations of FGM beam for post-buckling problem were found by applying Hamilton principle and Navier type solution method was used to solve post-buckling problem. It is assumed that elasticity modulus is changing in the thickness direction and all other material properties are taken to be constant. Variation of elasticity modulus in the thickness direction, are described by a simple power law distribution in terms of the volume fractions of constituents. The shear effect is shown to have a significant contribution to both the buckling and post-buckling behaviors. Results of this analysis show that classical and first-order theories underestimate the amplitude of buckling while all higher order theories, considered in this study, yield very close results for the static post-buckling response.