**2.17 Elastic stability of curved nanobeam by finite element approach**

The elastic stability of curved nanobeam had been investigated using Eringen's strain driven model [19] coupled with higher order shear deformation theory. The influence of different structural theories and analyses of nanobeam is taken into account while deducing the model. The governing differential equation is solved by finite element method using 3 –noded curved beam. The model had been validated using analytical/numerical solutions. The parameters such as thickness ratio, beam length, rise of curved beam, boundary conditions and size dependent [19] or nonlocal are analyzed based on buckling behavior of curved nanobeams. The results prove that the type of buckling mode corresponding to lowest critical value would be varying based on geometrical and internal material length scale parameter and boundary conditions [19].

#### **2.18 Tensile modulus of CNT reinforced polypropylene composite**

The reinforcing efficiency of carbon nanotubes (CNTs) in polymers had been found using finite element modeling. The probability distribution functions [20] of CNT diameter, orientation, dispersion and waviness had been incorporated in the

finite element model to derive how the CNT characteristics affect the tensile modulus of CNT reinforced polypropylene composite. The scanning electron microscopy images of CNT/PP composites made by melt mixing and injection molding had been used by image analysis approach [20]. The predicted model had been found to be experimentally correct as per ASTM D638.
