Elasticity Solution of Functionally Graded Carbon Nanotube Reinforced Composite Cylindrical Panel

Abstract

Based on three-dimensional theory of elasticity, static analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel subjected to mechanical uniformed load with simply supported boundary conditions is carried out. In the process, stress and displacement fields are expanded according to the Fourier series along the axial and circumferential coordinates. From constitutive law, stress-displacement relations and equilibrium equations, state space equation is obtained. The obtained first order governing differential equations can be solved analytically. The effects of CNT distribution cases, the volume fraction of CNT, length to mid radius ratio, span of the cylindrical panel, variation of mechanical load and radius to thickness ratio on the bending behaviour of the cylindrical panel are examined. It should be noted that by using Fourier series solution it is possible only to solve the static behaviour of cylindrical panel with simply supported for all of edges and for the non-simply supported boundary conditions it is possible to solve numerically. The obtained analytical solution can be used to validate the results of approximate two dimensional conventional theories.