Elastodynamic Potential Method for Transversely Isotropic Solid

In this paper, an analytical solution for the axisymmetric interaction of a rigid disc inclusion embedded in bonded contact with the surfaces of a penny-shaped crack and a transversely isotropic medium is investigated. By using a method of potential functions and treating dual and triple integral equations, the mixed boundary value problem is written in the form of two coupled integral equations, which are amenable to numerical treatments. The axial stiffness of the inclusion and the shearing stress intensity factor at the tip of the penny-shaped crack for different degrees of material anisotropy are illustrated graphically. Useful limiting cases such as a rigid disc inclusion in an uncracked medium and in a completely cracked solid are recovered.

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“…The displacement and stress fields for a semi-infinite transversely isotropic medium (0 ≤ z < ∞) are as below [31] …”

Section: Statement Of the Problem And The Governing Equationsmentioning

confidence: 99%

Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

2017

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“…The material properties are given in Table II, where E and E′ are the Young's moduli in the plane of isotopy and perpendicular to it; ν is Poison's ratio that characterize the effect of horizontal strain on the complementary vertical strain; ν′ is the Poisson's ratio which characterize the effect of vertical strain on the horizontal one; and c 44 stands for the shear modulus for the plane normal to the plane of isotropy. Detailed relations of these material parameters to the transverse isotropic elasticity tensor, c ij can be found in [35]. For the materials considered, the restrictions …”

Section: Lateral Soil-pile Interaction Formulationmentioning

confidence: 99%

Rigid cylinder in a transversely isotropic half‐space under lateral loads

Shahmohamadi

Khojasteh

Rahimian

et al. 2011

Num Anal Meth Geomechanics

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SUMMARYA boundary integral equation method is presented for a rigid cylindrical pipe-pile of finite length embedded in a transversely isotropic half-space under lateral loads. In the framework of three-dimensional elastostatics, the complicated soil-structure interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit. By means of a complicated numerical procedure, detailed results on the three-dimensional load-transfer process are provided for benchmark comparison and practical applications.

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“…For a half-space, the foregoing requirements must be appended by the regularity condition at infinity that → 0 as √ r 2 + z 2 →∞. The equations of equilibrium for a homogeneous transversely isotropic elastic solid in terms of displacements and in the absence of body forces in the case of axisymmetric can be expressed as [21] …”

Section: Statement Of the Problem And The Governing Equationmentioning

confidence: 99%

“…By means of Equation (10) and the identities involving Hankel transforms, the transformed displacement-potential relations may be expressed compactly as [21] …”

Section: Statement Of the Problem And The Governing Equationmentioning

confidence: 99%

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

Katebi

Khojasteh

Rahimian

et al. 2010

Num Anal Meth Geomechanics

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SUMMARYA theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half-space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary-layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response.

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Elastodynamic Potential Method for Transversely Isotropic Solid

Cited by 102 publications

References 13 publications

Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

Rigid cylinder in a transversely isotropic half‐space under lateral loads

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

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