Bending and free vibration analyses of CNTRC shell structures considering agglomeration effects with through-the-thickness stretch

The present work investigates an enhanced finite element model and numerical analysis to illustrate the agglomeration effect of Carbon Nanotubes (CNTs) on static and free vibration responses of reinforced composite plate and cylindrical panel shell. The developed model is based on the kinematics of the improved first-order-shear deformation theory (FSDT), assuming a parabolic variation of the transverse shear strains and fulfilling the zero circumstance of the transverse shear stresses at the extreme structure’ surfaces omitting the use of shear correction factors. The material properties of the nanocomposite are determined using a developed micromechanical model based on the Mori–Tanaka approach. The developed finite element formulation is based on three-dimensional constitutive equations without reduction involving the addition of one parameter of thickness change combined with the Enhanced Assumed Strain (EAS) method. Four enhancement models are established and discussed. In a first attempt, the improvement of the third bending strain using one or four parameters are presented. In a second attempt, the membrane strain is enhanced with four parameters. Due to lack of investigations on structural behavior of composite structures reinforced with agglomerated CNTs, new static and free vibration results for shell structures with three level of CNT agglomeration are examined. Parametric studies are here in developed to present the influences of the characteristic parameters on the structural behavior of the CNTRC shell in a new graphic way; such as the volume fraction and agglomeration of nanofibers, geometrical parameters, and boundary conditions. Based on numerical results, it is found that the agglomeration and distributions of the reinforcing fibers are really crucial and play a significant role on the static and vibrational performances of the structure. •Static and free vibration behavior analysis of Carbon Nanotubes Reinforced Composite (CNTRC) shell structures with agglomerated CNTs.•Using Mori–Tanaka’s approach to examine the effect of clustered CNTs.•3D bending strain accounting for through-the-thickness stretching.•Extensible modified First Order Shear Deformation Theory (FSDT).•The improvement of the third bending strain using the ANS and EAS methods.