M. Mirzaei

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

Summary During the past five years, it has been shown that carbon nanotubes act as an exceptional reinforcement for composites. For this reason, a large number of investigations have been devoted to analysis of fundamental, structural behavior of solid structures made of carbon-nanotube-reinforced composites (CNTRC). The present research, as an extension of the available works on the vibration analysis of CNTRC structures, examines the free vibration characteristics of plates containing a cutout that are reinforced with uniform or nonuniform distribution of carbon nanotubes. The first-order shear deformation plate theory is used to estimate the kinematics of the plate. The solution method is based on the Ritz method with Chebyshev basis polynomials. Such a solution method is suitable for arbitrary in-plane and out-of-plane boundary conditions of the plate. It is shown that through a functionally graded distribution of carbon nanotubes across the thickness of the plate, the fundamental frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement.

Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.

Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes

ABSTRACT In this work, the problem of thermal buckling of composite plates reinforced with carbon nanotubes (CNTs) is investigated. Distribution of CNTs as reinforcements through the thickness direction of the plate is assumed to be either uniform or functionally graded (FG). Properties of the reinforcement and matrix are both temperature dependent. Properties of the composite media are obtained according to a refined rule of mixture approach where the efficiency parameters are introduced. The plate is in a super elliptical shape where the simple elliptical shape and rectangular shapes are obtained as especial cases. In these types of plates due to the round corners, stress concentration phenomenon is eliminated. Based on the Ritz method where the shape functions are of the polynomial type, the governing equations are obtained. These equations are solved using an iterative eigenvalue problem since the properties are temperature dependent. Numerical results are validated for the simple case of an isotropic plate. Novel numerical results are provided for plates reinforced with CNTs in different shapes, various volume fractions and different patterns of CNT distribution. It is shown that FG-X pattern of CNTs in matrix results in the maximum critical buckling temperature.