Owing to their superior mechanical and thermal properties, carbon nanotube (CNT) reinforced composite materials have wide range of applications in various technical areas such as aerospace, automobile, chemical, structural and energy. In this paper, the nonlinear axisymmetric dynamic behavior of sandwich spherical and conical shells made up of CNT reinforced facesheets is studied. The shell is subjected to thermal loads and discretized with three-noded axisymmetric curved shell element based on field consistency approach. The in-plane and the rotary inertia effects are included within the transverse shear deformation theory in the element formulation. The present model is validated with the available analytical solutions from the literature. A detailed parametric study is carried out to showcase the effects of the shell geometry, the volume fraction of the CNT, the core-to-face sheet thickness and the environment temperature on the dynamic buckling thermal load of spherical caps. © 2017 World Scientific Publishing Company.

Sundararajan Natarajan

Department of Mechanical Engineering

A. Sankar

T. Merzouki

M. Ganapathi

AUTOMOBILE MATERIALS

Buckling

Nanotubes

Reinforcement

Sandwich structures

Shear deformation

Shear flow

Shells (structures)

Spheres

Thermal load

Yarn

Axisymmetric

CARBON NANOTUBE REINFORCEMENTS

Non-linear response

Sandwich shells

SHEAR FLEXIBLE ELEMENTS

SNAP-THROUGH

SPHERICAL CAPS

Carbon nanotubes

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Nonlinear Dynamic Thermal Buckling of Sandwich Spherical and Conical Shells with CNT Reinforced Facesheets

International Journal of Structural Stability and Dynamics

In this paper, the supersonic flutter characteristics of doubly curved sandwich shell panels, viz., cylindrical and spherical shells, with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible shell element developed based on higher-order structural theory. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacement at the interface. The strain-displacement relation is accurately introduced in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange's equation of motion, are obtained by QR algorithm. The accuracy of the present formulation is validated considering the problems for which solutions are available in the literature. A detailed numerical study is conducted to highlight the significance of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the shell thickness and the aspect ratio, radius-to-thickness ratio, and temperature on the flutter boundaries. © 2015 Elsevier Ltd.

Composite Structures

Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory

The dynamic axisymmetric behavior of clamped laminated composite spherical caps subjected to suddenly applied loads is investigated using an eight-noded quadrilateral doubly curved shear flexible shell element based on the field-consistency approach. Geometric nonlinearity is considered using von Karman’s strain-displacement relations. The solution is obtained using the Wilson- θ numerical integration scheme. The pressure corresponding to a sudden jump in the maximum average deflection in the time history of the shell structure is taken as dynamic buckling pressure. A detailed parametric study is carried out to bring out the effects of shell geometries and material properties, number of layers, lamination schemes, and type of loading on a dynamic buckling load. © 1995 by ASME.

Journal of Applied Mechanics, Transactions ASME

Dynamic buckling of laminated anisotropic spherical caps

Supersonic flutter analysis of laminated composite circular cylindrical shells is investigated by using an axisymmetric shell finite element based on the field-consistency approach. The formulation includes transverse shear deformation and in-plane and rotary inertia effects. The aerodynamic force is evaluated by considering the first order high Mach number approximation to linear potential flow theory. The solution for the complex eigenvalue problem is obtained by the QR algorithm. Numerical results are presented for isotropic, orthotropic and laminated anisotropic circular cylindrical shells. A detailed parametric study is carried out to observe the effects of aspect ratio, thickness, internal pressure, axial compression, number of layers and lamination scheme on the flutter boundary. © 1994 Academic Press. All rights reserved.

Journal of Sound and Vibration

Field-Consistent Element Applied to Flutter Analysis of Circular Cylindrical Shells

The dynamic axisymmetric behaviour of clamped orthotropic shallow spherical shell subjected to instantaneously applied uniform step-pressure load of infinite duration, is investigated here. The available modal equations, based on an assumed two-term mode shape for the lateral displacement, for the free flexural vibrations of an orthotropic shallow spherical shell is extended now for the forced oscillations. The resulting modal equations, two in number, are numerically integrated using Runge-Kutta method, and hence the load-deflection curves are plotted. The pressure corresponding to a sudden jump in the maximum deflection (at the apex) is considered as the dynamic buckling pressure, and these values are found for various values of geometric parameters and one value of orthotropic parameter. The numerical results are also determined for the isotropic case and they agree very well with the previous available results. It is observed here that the dynamic buckling load increases with the increase in the orthotropic parameter value. The effect of damping on the dynamic buckling load is also studied and this effect is found to increase the dynamic buckling load. It is further observed that this effect is more pronounced with increase in the rise of the shell. © 1982.

Computers and Structures

Dynamic buckling of orthotropic shallow spherical shells

The axisymmetric dynamic behaviour of clamped isotropic and orthotropic spherical cap with central circular hole under a uniform step pressure of infinite duration is investigated. The critical loads are determined by using the rapidly converging Chebyshev series in a space domain and a Houbolt numerical integration scheme in time domain. Three different cases of openings are investigated and detailed numerical results have been obtained for the isotropic case and two different cases of orthotrophy, which may be useful for design engineers. © 1979.

International Journal of Mechanical Sciences

Dynamic buckling of isotropic and orthotropic shallow spherical cap with circular hole

Journal	International Journal of Structural Stability and Dynamics
Publisher	World Scientific Publishing Co. Pte Ltd
ISSN	02194554
Open Access	No