Green's function for a two–dimensional exponentially graded elastic medium

Chan, Youn-Sha; Gray, L. J.; Kaplan, T. A.; Paulino, Gláucio H.

doi:10.1098/rspa.2003.1220

Cited by 69 publications

(34 citation statements)

References 20 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We adopt a commonly used model for the material gradation: a spatially uniform Poisson's ratio and an exponential variation along the thickness coordinate z for the Young modulus (see, e.g., Erdogan 1995;Kashtalyan 2004). This choice of gradation has been made by Martin et al (2002) and Chan et al (2004) for solving elastic problems by means of the boundary element method.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional elastic solutions for functionally graded circular plates

Sburlati¹,

Bardella²

2011

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Three-dimensional elastic solutions are obtained for a functionally graded thick circular plate subject to axisymmetric conditions. We consider a isotropic material where the Young modulus depends exponentially on the position along the thickness, while the Poisson ratio is constant. The solution method utilises a Plevako's representation form which reduces the problem to the construction of a potential function satisfying a linear fourth-order partial differential equation. We write this potential function in terms of Bessel functions and we pointwise assign mixed boundary conditions. The analytic solution is obtained in a general form and explicitly presented by assuming transversal load on the upper face and zero displacements on the mantle; this is done by superposing the solutions of problems with suitably imposed radial displacement. We validate the solution by means of a finite element approach; in this way, we highlight the effects of the material inhomogeneity and the limits of the employed numerical method near the mantle, where the solution shows a large sensitivity to the boundary conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

Three-dimensional elastic solutions for functionally graded circular plates

Sburlati¹,

Bardella²

2011

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

show abstract

“…1,2,3,4,5,6 Notable examples include disorder-induced localized states (i.e., the Anderson localization of lattice vibrations), fractal-induced localization (i.e., fractons 7 ), modes contributing the boson peak, 8 the connection of excess of low-frequency modes with the jamming-unjamming transition in particle packings, 9 intrinsic localized modes (ILMs)…”

Section: Introductionmentioning

confidence: 99%

Harmonic vibrational excitations in graded elastic networks: Transition from phonons to gradons

Xiao

Yakubo

2006

Phys. Rev. B

View full text Add to dashboard Cite

We have identified a new type of transition from extended to localized vibrational states in onedimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearestcoupling force constants vary linearly along the chain. We found that the delocalization transition occurs at the maximum frequency of the corresponding homogeneous chain, which is in a continuous single band.Although each state in the localized phase, called gradon, can be regarded as an impurity localized mode, the localization profile is clearly distinct from usual impurity modes or the Anderson localized modes. We also argue how gradons may affect the macroscopic properties of graded systems. Our results can provide insights into many analogous systems with graded characters.

show abstract

“…For a detailed review of studies in the eld of anisotropic and nonhomogeneous isotropic materials, one might refer to [2]. The fundamental solutions concerning the exponentially graded elastic solids may be found in [3][4][5][6][7][8]. Esandari and Shodja [9] obtained fundamental solutions to an exponentially graded transversely isotropic half-space for arbitrary buried static loads.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional axisymmetric responses of exponentially graded transversely isotropic tri-materials under interfacial loading

et al. 2017

View full text Add to dashboard Cite

Abstract. In this paper, an analytical formulation is presented to study an exponentially graded transversely isotropic tri-material under applied axisymmetric point-load and patchload with the aid of Hankel transform and use of a potential function. The given formulation is shown to be reducible to the special cases of (1) an inhomogeneous nite layer on a rigid base; (2) exponentially graded bi-material or half-space under applied buried loads; (3) homogeneous tri-material or bi-material solid. Several numerical solutions are presented to explain inhomogeneity e ect on the stress transfer process in the inhomogeneous threelayered medium by means of a fast and accurate numerical method.

show abstract

Green's function for a two–dimensional exponentially graded elastic medium

Cited by 69 publications

References 20 publications

Three-dimensional elastic solutions for functionally graded circular plates

Three-dimensional elastic solutions for functionally graded circular plates

Harmonic vibrational excitations in graded elastic networks: Transition from phonons to gradons

Three-dimensional axisymmetric responses of exponentially graded transversely isotropic tri-materials under interfacial loading

Contact Info

Product

Resources

About