Static Bending Behavior of FG-CNT Reinforced Composite Plates Using Higher Order Shear Deformation Theory

Abstract

The analytical formulations and solutions for the bending behavior of simply supported functionally graded carbon nanotube reinforced composite plates (FG-CNT Plates) are presented in this paper. Higher Order Shear Deformation Theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate is used for the analysis. Two types of carbon nanotube (CNT) distributions are analyzed in this investigation. It is assumed that through the thickness, the material properties of the plate are varied. The governing equations of motion and boundary conditions are derived based on the principle of virtual work. Solutions are obtained for FG-CNT Plates in closed-form using Navier's technique. The deflections and stresses are shown for simply supported boundary conditions. The effect of side-to-thickness ratio, aspect ratio, the volume fraction, and through-the-thickness on the deflections and stresses are studied in this paper. The obtained results are compared with the available FSDT solutions in the literature for deflections. This research also shows that the volume fraction of CNT has little effect on stresses. A computer program in C is developed for determining deflections and stresses. Keywords: Static Bending Behavior, FG-CNT Plates, Effective Material Properties, HSDT, Navier's Method. I. INTRODUCTIONIn 1987, Niino and co-workers proposed initially the concept of functionally graded materials(FGMs) [1]. Functionally graded materials available in nature as bones, teeth etc. [2], that are designed by nature to meet their expected service requirements. This concept is reproduced from nature to solve an engineering problem. Functionally graded materials (FGMs) are gaining interest from researchers during recent years since these are advanced materials which show improvement in properties like thermal, mechanical, light-weight, dimensional stability, barrier properties, flame retardancy, heat resistance and electrical conductivity [3][4]. Initially, FGMs were utilized as thermal barrier materials for aerospace structural applications and fusion reactors [5]. FGMs also found significance in structural components functioning under very high-temperature environments [6]. As the content of reinforcement in FGMs varies gradually in some direction leads to gradation in properties through the thickness of plate thus eliminates interface problems and reduces stress concentrations [7]. The carbon nanotubes have great stiffness and axial strength due to carbon-carbon Sp2 bonding. They are the excellent stiff materials [8] with Young's modulus of 1.4 TPa and tensile strength well above 100 GPa. The CNT reinforced functionally graded composite materials(FGCM) having a wide variety of applications in different technological areas such as aerospace, defence, energy, automobile, medicine, structural and chemical industry [9]. Researchers have been proposed a variety of plate theories to interpret the behavior of plates earlier. It is helpful to discuss some developments in plate theory a...