The bending analysis of functionally graded carbon nanotube (CNT) reinforced doubly curved singly ruled truncated rhombic cone is investigated. In this study, a simple C⁰ isoparametric finite element formulation based on third order shear deformation theory is presented. To characterize the membrane-flexure behavior observed in a CNT reinforced truncated rhombic cone, a displacement field involving higher-order terms in in-plane fields is considered. The proposed kinematics field incorporates for transverse shear deformation and nonlinear variation of the in-plane displacement field through the thickness to predict the overall response of the CNT reinforced truncated rhombic cone in an accurate sense. The material properties of the CNT reinforced truncated rhombic cone are estimated according to the rule of mixture. The present model eliminates the need of shear correction factor and imposed zero-transverse shear strain at upper and lower surface of the truncated rhombic cone. The new feature in present model is simultaneous inclusion of twist curvature in strain field as well as curvature in displacement field that makes it suitable for moderately thick and deep truncated rhombic cone. The proposed new mathematical model is implemented in finite element code written in FORTRAN. The proposed model has been validated with analytical, experimental, and finite element results from the literature. This is first attempt to study bending response of CNT reinforced doubly curved singly ruled truncated rhombic cone. The effect of CNT distribution, boundary condition, loading pattern, and other geometric parameters are also examined.

This paper examines the effect of uniaxially aligned carbon nanotube (CNT) on flexural and free vibration analysis of CNT-reinforced functionally graded plate. The mathematical model includes expansion of Taylor’s series up to the third degree in the thickness co-ordinate. Since there is a parabolic variation in transverse shear strain deformation across the thickness co-ordinate, the shear correction factor is not necessary. A nine-node two-dimensional (2D) C⁰ isoparametric element containing seven nodal unknowns per node was developed in the finite element code. The final material properties of CNT-reinforced functionally graded plate are estimated using the extended rule of mixture. The effect of CNT distribution, boundary condition, volume fraction and loading pattern are studied by developing a finite element code. An additional finite element code was developed for the study of the influence of concentrated mass on free vibration analysis of CNT-reinforced functionally graded plate.

The present study focuses on the static and dynamic response of functionally graded carbon nanotube (FG-CNT)-reinforced rhombic laminates. The cubic variation of thickness coordinate in the displacement field is considered in terms of Taylor’s series expansion, which represents the higher-order transverse cross-sectional deformation modes. The condition of zero-transverse shear strain at upper and lower surface of FG-CNT-reinforced rhombic laminates is imposed in the present formulation. The present two-dimensional model is formulated in a finite element, with the C⁰ element consisting of seven nodal unknowns per node. The final material properties of FG-CNT-reinforced rhombic laminates are estimated using the rule of mixture. The obtained numerical are compared with the results available in the literature to verify the reliability of the present model. The present study investigates the effect of CNT distribution, loading pattern, volume fraction, and various combinations of boundary constraints by developing a finite element code in FORTRAN.

The flexural analysis of functionally graded carbon nanotube (CNT)-reinforced doubly curved singly ruled composite truncated cone is studied. The mathematical model contains the expansion of Taylor’s series up to third degree of thickness coordinate and normal curvatures in in-plane displacement fields. Because the distribution of transverse shear strain across the thickness coordinate is parabolic, the need of shear correction factor is removed. The condition of zero-transverse shear strain at the upper and lower surface of the truncated cone is applied in the present formulation. The advancement in the present mathematical model is the simultaneous inclusion of normal curvatures in deformation field and twist curvature in strain-displacement equations. The proposed new mathematical model is implemented in finite-element code written in FORTRAN. The present results are in good agreement with the experimental results as well as results from other methods. After validation, a large number of flexural problems are presented by varying different boundary conditions, volume fraction, loading pattern, and geometric parameters.