A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

Abstract

The elastic analysis of a pressurized functionally graded material (FGM) annulus or tube is made in this paper. Different from existing studies, this study deals with an axisymmetrical FGM hollow cylinder or disk with arbitrarily varying material properties. A simple and efficient approach is suggested, which reduces the associated problem to solving a Fredholm integral equation. The resulting equation is approximately solved by expanding the solution as series of Legendre polynomials. The stresses and displacements can be represented in terms of the solution to the equation. For radius-dependent Young's modulus, numerical results of the distribution of the radial and circumferential stresses are presented graphically. Our results indicate that change in the gradient of the FGM tube does not produce a substantial variation of the radial stress, but strongly affects the distribution of the hoop stress. In particular, the hoop stress may reach its maximum at an internal position or at the outer surface when the tube is internally pressurized. The results obtained are helpful in designing FGM cylindrical vessels to prevent failure.

Analysis of functionally graded thick truncated cone with finite length under hydrostatic internal pressure

“…Comparison of the stress components in an internally pressurized FG hollow cylinder [3] where p is the internal hydrostatic pressure, and p r , p z are the components of internal pressure in direction of r and z, respectively. …”

“…Now by assembling element matrices, the global matrix equation for the truncated thick hollow cone can be obtained as[K ]{δ} = {F}(16)To verify the present work, two examples of a FG thick hollow cylinder of Ref [3]. and isotropic truncated thick conical shell of Ref [10].…”

Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

“…Recently, many research works have been devoted to the hollow circular cylinder problem for FGMs [Zhang and Hasebe 1999;Shao 2005;Dryden and Jayaraman 2006;Shi et al 2007;Tutuncu 2007;Batra and Iaccarino 2008;Chen and Lin 2008;Theotokoglou and Stampouloglou 2008;Li and Peng 2009]. In most of the studies, the Young's modulus is assumed in the form of exponential or power law functions.…”

“…For example, the associated elastic problem is reduced to a Fredholm integral equation. By approximately solving the resulting equation, the distributions of the radial and circumferential stresses can be determined [Li and Peng 2009].…”

Rotating Variable-Thickness Inhomogeneous Cylinders: Part I—Analytical Elastic Solutions

“…The effect of varying Poisson's ratio on deformation fields in FG cylinders has been investigated by Mohammadi and Dryden [10]. Li and Peng [11] have analyzed axisymmetric deformations of FG hollow cylinders and disks with arbitrarily varying material properties.…”