**Journal of Theoretical**

and Applied Mechanics

and Applied Mechanics

**56**, 3, pp. 701-712, Warsaw 2018

DOI: 10.15632/jtam-pl.56.3.701

### Mechanical buckling of functionally graded polyethylene/clay nanocomposites columns based on the Engesser-Timoshenko beam theory

functionally graded and uniformly distributed of nanoclay subjected to axial compressive

load with simply supported conditions at both ends. The Young moduli of functionally

graded and uniformly distributed nanocomposites are calculated using a genetic algorithm

procedure and then compared with experimental results. The formulation is modified to

include the effect of nanoparticles weight fractions in the calculation of the Young modulus

for uniform distribution. Also, it is modified to take into account the Young modulus as

a function of the thickness coordinate. The displacement field of the beam is assumed ba-

sed on the Engesser-Timoshenko beam theory. Applying the Hamilton principle, governing

equations are derived. The influence of nanoparticles on the buckling load of the beam is

presented. To investigate the accuracy of the present analysis, a compression study with the

experimental results is carried out.

*Keywords*: mechanical buckling, functionally graded nanocomposite, montmorillonite, gene- tic algorithm theory

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