Three-dimensional stress distributions in hexagonal aeolotropic crystals

Elliott, Harold; Mott, N. F.

doi:10.1017/s0305004100024531

Cited by 306 publications

(121 citation statements)

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“…Thus, if 12) then (3.10) will be satisfied. Thus, when g satisfies the system (3.12), the transformation given by (3.8) transforms the linear system with variable coefficients (3.7) to the linear system with constant coefficients (3.11).…”

Section: Basic Equationsmentioning

confidence: 99%

“…Thus, the analysis of the previous two sections may be applied to an inhomogeneous isotropic material for which the Poisson's ratio ν is 1/4 (a frequently occurring value in rock materials (14)) and the inhomogeneity is specified by either Young's modulus or one of the Lamé coefficients in the forms 11) where these alternative forms are related by 12) so that…”

Section: An Isotropic Half-space and Layer On A Rigid Foundationmentioning

confidence: 99%

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Axisymmetric Loading of a Class of Inhomogeneous Transversely Isotropic Half-Spaces with Quadratic Elastic Moduli

Clements

Kusuma

2010

The Quarterly Journal of Mechanics and Applied Mathematics

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SummarySome axisymmetric problems are considered for a class of inhomogeneous anisotropic elastic materials for which the elastic moduli vary continuously as a quadratic function of the spatial coordinates. For a restricted class of transversely isotropic materials, loading of a half-space and a layer on a rigid foundation are considered and integral expressions for the displacement and stress are obtained. Particular attention is given to cases when the values of the elastic moduli near to the plane boundary of the half-space and the layer approach zero. Numerical results are obtained for some example transversely isotropic and isotropic materials.

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Section: Basic Equationsmentioning

confidence: 99%

Section: An Isotropic Half-space and Layer On A Rigid Foundationmentioning

confidence: 99%

Axisymmetric Loading of a Class of Inhomogeneous Transversely Isotropic Half-Spaces with Quadratic Elastic Moduli

Clements

Kusuma

2010

The Quarterly Journal of Mechanics and Applied Mathematics

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“…1. A potential function formulation was first given by Elliot (1948). The notation of Fabrikant (1989) is presently adopted.…”

Section: Potentialmentioning

confidence: 99%

“…The present potential function formulation for transversely isotropic materials (where the isotropic planes are parallel to the free surface) was de-veloped by Elliot (1948). It was put in its present form by Fabrikant (1989).…”

Section: Introductionmentioning

confidence: 99%

Love’s circular patch problem revisited: closed form solutions for transverse isotropy and shear loading

Hanson¹,

Puja²

1996

Quart. Appl. Math.

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Abstract.This paper considers the title problem of uniform pressure or shear traction applied over a circular area on the surface of an elastic half space. The half space is transversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is adopted where the elastic field is written in terms of three harmonic functions. The known point force potential functions are used to find the solution for uniform pressure or shear traction over a circular area by quadrature.Using methods developed by Love (1929) and Fabrikant (1988), the elastic displacement and stress fields for normal and shear loading are evaluated in terms of closed form expressions containing complete elliptic integrals of the first, second, and third kinds. The solution for uniform normal pressure on an isotropic half space was previously found by Love (1929). The present results for transverse isotropy including shear loading are new. During the course of this research, a new relation has been discovered between different forms of the complete elliptic integral of the third kind. This has allowed the present solution to be put in a more convenient form than that used by Love. Following a limiting procedure allows the isotropic solution to be obtained.It is shown that for normal loading the present results agree with Love's solution, while the results for shear loading of an isotropic half space are also apparently new. Special consideration is also given to derive the limiting form of the elastic field on the z-axis and the surface (z = 0).

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“…Many metallic substances and fiber-reinforced composites are described as being transversely isotropic and have five elastic constants [2,3]. A metallic shaft tends to produce material anisotropy after being placed in service in a radioactive environment.…”

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confidence: 99%