The radially nonhomogeneous elastic axisymmentric problem

Theotokoglou, Efstathios E.; Stampouloglou, I. H.

doi:10.1016/j.ijsolstr.2008.08.011

Cited by 49 publications

(24 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In previous studies on FGM hollow cylinders, the Young's modulus of the cylindrical tube is often assumed to obey a special law, while Poisson's ratio is an unchanged constant. For example, a radial inhomogeneity assumption of power-law form is frequently adopted in [6,[15][16][17][18], etc. For the case where Young's modulus is dominated by E 0 r β (r being the radial coordinate of the cylinder), an exact closed-form solution has been derived for a pressurized hollow cylinder in [16,19], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…For the case where Young's modulus is dominated by E 0 r β (r being the radial coordinate of the cylinder), an exact closed-form solution has been derived for a pressurized hollow cylinder in [16,19], respectively. More recently, for other cases with constant Poisson's ratio and varying Young's modulus including E(r) = Ar + B (A and B being material constants), E(r) = E 0 e βr (E 0 and β being material constants), the elastic behaviors of a hollow cylindrical pressure vessel have been studied by using special functions and series expansion in [2,18,20,21]. A cylinder with an exponentially varying elastic modulus along the radial coordinate and a constant Poisson's ratio has also been analyzed with application of the Michell stress function in [22].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

Peng

2009

J Elasticity

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

Peng

2009

J Elasticity

View full text Add to dashboard Cite

show abstract

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

2011

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

This paper provides a general solution for a multiply-layered cylinder made of functionally graded materials. The Young's modulus is assumed to be an arbitrary function of r , and the Poisson's ratio takes a constant value. The first step is to study the single-layer case (a < r < b). A transfer matrix is defined, relating the values of radial stress and displacement at the initial point (r = a) to those at the end point (r = b). The matrix is evaluated on the basis of two fundamental solutions, which are evaluated numerically. The final solution is obtained by using many transfer matrices for layers, continuation conditions between layers, and boundary conditions at inner and outer boundaries. Several numerical examples are provided.

show abstract

“…Tutuncu [8] has gave the power series solution for stresses and displacements in FG cylinders with exponentially-varying elastic modulus through the radial direction. Theotokoglou and Stampouloglou [9] have studied axisymmetric problems for radially inhomogeneous circular cylinders. The effect of varying Poisson's ratio on deformation fields in FG cylinders has been investigated by Mohammadi and Dryden [10].…”

Section: Introductionmentioning

confidence: 99%

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

Zenkour¹

2010

View full text Add to dashboard Cite

In this paper, an analytical solution for the rotation problem of an inhomogeneous hollow cylinder with variable thickness under plane strain assumption is developed. The present cylinder is made of a fiberreinforced viscoelastic inhomogeneous orthotropic material. The thickness of the cylinder is taken as parabolic function in the radial direction. The elastic properties varies in the same manner as the thickness of the cylinder while the density varies according to an exponential law form. The inner and outer surfaces of the cylinder are considered to have combinations of free and clamped boundary conditions. Analytical solutions are given according to different types of the hollow cylinders. An extension of the present solutions to the viscoelastic ones and some applications are investigated in Part II.

show abstract

The radially nonhomogeneous elastic axisymmentric problem

Cited by 49 publications

References 19 publications

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

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

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

Contact Info

Product

Resources

About