Two dimensional kinematic models for CNT reinforced sandwich cylindrical panels with accurate transverse interlaminar shear stress estimation

A comparative assessment of two sets of refined higher order theories, one with only shear deformation and another with both shear and normal deformations, is presented for the first time for the thin and moderately thick, CNT-reinforced cylindrical shell panels. The comparisons are also made with simple first order shear deformation theory (FSDT). The governing equations for static and free vibration analyses are systematically derived using a variational principle and solved analytically using Navier’s method. Effective material properties are evaluated using extended rule of mixture for continuously graded CNT fibres in thickness direction. Efficiency parameters are adopted from existing literature to effectively map the nano-scale CNT properties to macro-scale polymer matrix. Transverse shear stresses are recovered using the popular three-dimensional (3D) elasticity equilibrium equations, though there are issues with this scheme which are documented elsewhere, and a comparison with direct constitutive relations’ based evaluation is made. Results highlight the utility of thickness stretching kinematic models and advantage of one-step recovery procedure over a priori-constrained shear traction model. The computational advantage of higher order shear deformation theory make them more suitable for thin and low volume fraction nanocomposites. The estimates of FSDT suffer from significant errors for these heterogeneous materials. The benchmark results using refined shear and normal deformation model are presented for CNT-reinforced sandwich cylindrical panels. The dependence of volume fraction and geometrical parameters on the stress and free vibration response is also studied. •Higher order shell theory considering transverse shear deformation and thickness stretching effects is implemented to nanocomposites.•The extended rule of mixture-based homogenization scheme is adopted for evaluating effective properties of composite.•The thin and thick shell models are distinctly represented by Flugge–Lur’e–Byrne thickness criterion.•The effect of continuous gradation of CNT reinforcement is studied and X-type gradation is found to be most effective in increasing stiffness.•Transverse shear stresses are accurately evaluated using 3D equilibrium equations.