The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

doi:10.1177/1081286516635871

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The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

Journal Article•DOI•

The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

M. Shahmohamadi¹, Ali Khojasteh¹, Mohammad Rahimian¹, Ronald Y. S. Pak²•Institutions (2)

University of Tehran¹, University of Colorado Boulder²

01 Jun 2017-Mathematics and Mechanics of Solids (SAGE Publications)-Vol. 22, Iss: 6, pp 1081286516635871

TL;DR: In this article, a rigorous formulation for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium is presented, where the materials are considered to be linearly elastic transversely isotropic materials and the exponential variation of properties along the depth of each layer is assumed to model the effect of inhomogeneity.

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Abstract: A rigorous formulation is presented for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium. The materials are considered to be linearly elastic transversely isotropic materials and the exponential variation of properties along the depth of each layer is assumed in order to model the effect of inhomogeneity. The disk is considered to be at the top of the coating layer or embedded at the interface of the two media. By satisfying the boundary conditions, the problem leads to a dual integral equation and is reducible to a Fredholm integral equation of the second kind which is solved numerically. The numerical solutions survey the effect of material inhomogeneity through two special cases: a functionally graded coating on a homogeneous transversely isotropic half-space and a homogeneous transversely isotropic coating on an inhomogeneous half-space. The accuracy of the numerical solutions is verified by comparison with the corresponding solution for homogeneous mat...

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Journal Article•DOI•

Vertical Dynamic Response of Rigid Circular Foundation in Multilayered Transversely Isotropic Poroelastic Half-Space

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Suraparb Keawsawasvong¹, Teerapong Senjuntichai²•Institutions (2)

Thammasat University¹, Chulalongkorn University²

04 May 2021-International Journal of Structural Stability and Dynamics

TL;DR: In this article, the influence of anisotropic properties and layering of saturated soils on dynamic response of a circular foundation under time-harmonic vertical loading is studied, where the foundation is constructed with a linear lattice.

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Abstract: The influence of anisotropic properties and layering of saturated soils on dynamic response of a circular foundation under time-harmonic vertical loading is studied in this paper. The foundation is...

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10 citations

Journal Article•DOI•

Soil-pile interaction in inhomogeneous transversely isotropic media

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H. Abdorazaqi¹, Ali Khojasteh¹, Mohammad Rahimian¹, Ronald Y. S. Pak², M. Shahmohamadi¹ - Show less +1 more•Institutions (2)

University of Tehran¹, University of Colorado Boulder²

01 Jun 2019-Soils and Foundations

TL;DR: In this article, the axisymmetric interaction analysis of a thin-walled cylindrical pile with finite length embedded in an exponentially graded transversely isotropic half-space under axial loads at the top of pile is considered.

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4 citations

Journal Article•DOI•

Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space:

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Maziar Kalantari¹, Naser Khaji², Morteza Eskandari-Ghadi³•Institutions (3)

Tarbiat Modares University¹, Hiroshima University², University of Tehran³

01 Jul 2021-Mathematics and Mechanics of Solids

TL;DR: In this article, the authors have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure, and an equivalent static structure, for these kinds of structures, an equivalent dynamic a...

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Abstract: Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static a...

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4 citations

Cites background from "The frictionless axial interaction ..."

...[19] presented a rigorous formulation for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium under vertical load....
[...]

Journal Article•DOI•

Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space

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Maziar Kalantari, Naser Khaji, Morteza Eskandari-Ghadi, Suraparb Keawsawasvong

28 Mar 2022-Transportation infrastructure geotechnology

Journal Article•DOI•

Response of rigid circular plate in a functionally graded transversely isotropic, half-space under horizontal steady-state excitation

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Maziar Kalantari, Naser Khaji

26 Jul 2022-Mechanics Based Design of Structures and Machines

TL;DR: In this article , a theoretical formulation for lateral translation and impedance function of a rigid foundation in a transversely isotropic functionally graded (TIFG) half-space is presented, where the medium is considered linear elastic and the elastic constants of materials vary exponentially along the depth for considering the effect of elastic nonhomogeneities.

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Abstract: In this paper, a theoretical formulation for lateral translation and impedance function of a rigid foundation in a transversely isotropic functionally graded (TIFG) half-space is presented. Accordingly, the medium is considered linear elastic and the elastic constants of materials vary exponentially along the depth for considering the effect of elastic non-homogeneities. The relax treatment of mixed boundary value problem is formulated by integrating the transformed kernels of Green’s functions over the foundation area with unknown surface traction function, which can be reduced into a Fredholm integral equation. The results represent the impact and treatment of frequency and material anisotropy through the medium. In addition, static and dynamic distribution of tangential shear stress over the foundation for surface and embedded disk extracted and the cutoff frequency is found out explicitly. The proposed solution gives exact concurrence with accessible literature.

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References

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Book•

The use of integral transforms

[...]

Ian N. Sneddon

01 Jan 1972

1,808 citations

"The frictionless axial interaction ..." refers background in this paper

...By virtue of the zeroth-order Hankel transform for sufficiently regular function f (r, z) with respect to the radial coordinate [44] f̃ (ξ , z) = ∫ ∞...
[...]

Journal Article•DOI•

Modeling and Analysis of Functionally Graded Materials and Structures

[...]

Victor Birman¹, Larry W. Byrd²•Institutions (2)

Missouri University of Science and Technology¹, Wright-Patterson Air Force Base²

01 Sep 2007-Applied Mechanics Reviews

TL;DR: Diverse areas relevant to various aspects of theory and applications of FGM include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture.

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Abstract: This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

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1,008 citations

Additional excerpts

...developing the processing techniques, any special variation of properties may be obtained; however, for continuum mathematical modeling, generally the presumed relations such as linear, exponential, power-law, sigmoid, or the micromechanical approaches such as variational methods, Eshelby-type inclusion theories, percolation, multiple scattering theories, and so on [1], may be utilized (see also [2])....
[...]

Book•

Mixed boundary value problems in potential theory

[...]

Ian N. Sneddon, Joseph Gillis

01 Jan 1966

965 citations

"The frictionless axial interaction ..." refers background or methods in this paper

...Reduction to Fredholm integral equations The reduction of the previously obtained dual integral equations to the Fredholm integral equation is possible by the procedures in [46] or [47]....
[...]
...For the remaining boundary integral equation, following the procedure in [46] and using (45), the integral equation (37) may be reduced to a Fredholm integral equation of the second kind as...
[...]
...Next, an auxiliary functionψ is defined and to satisfy (38), with the consideration in [46] or some calculation abbreviated for brevity [47], the following formulation is considered:...
[...]

Journal Article•DOI•

Two-dimensional sliding frictional contact of functionally graded materials

[...]

Liao-Liang Ke¹, Yue-Sheng Wang¹•Institutions (1)

Beijing Jiaotong University¹

01 Jan 2007-European Journal of Mechanics A-solids

TL;DR: In this paper, a multi-layered model for sliding frictional contact analysis of functionally graded materials with arbitrarily varying shear modulus under plane strain-state deformation has been developed.

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Abstract: A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson's ratio is assumed to be a constant. In the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the stresses in the contact zone.

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188 citations

"The frictionless axial interaction ..." refers background in this paper

...Ke and Wang [17] presented a multi-layered simulation with the linear variation of material properties in each layer for the analysis of sliding frictional contact of FGM....
[...]
...Ke and Wang [26] considered normal and tangential loading for studying the fretting contact of two dissimilar materials with functionally graded coatings using the multi-layer concept and the linear variation of material properties to resemble the arbitrary spatial variation of properties....
[...]
...Ke and Wang [17] presented a multi-layered simulation with the linear variation of material properties in each layer for the analysis of sliding frictional contact of FGM. Guler and Erdogan [18] analyzed the contact of rigid indenters of different shapes with a graded isotropic coating layer on a homogeneous half-space....
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Journal Article•DOI•

The solution of Bessel function dual integral equations by a multiplying-factor method

[...]

B. Noble¹•Institutions (1)

Royal College of Science and Technology¹

01 Apr 1963

TL;DR: In this paper, the authors considered the dual integral equations where f(ρ), g(ρ) are given, A(t) is unknown, and α is a given constant.

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Abstract: In this paper we first of all consider the dual integral equationswhere f(ρ), g(ρ) are given, A(t) is unknown, and α is a given constant. This system, with g(ρ) = 0, was originally considered by Titchmarsh ((13), p. 337), and Busbridge (1), who obtained a solution by the use of Mellin transforms and analytic continuation in the complex plane. The method described in this paper involves the application of certain multiplying factors to the equations. In the present case it is relatively easy to guess the multiplying factors and then the method is essentially a real-variable technique. It is presented in this way in § 2 below.

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167 citations

"The frictionless axial interaction ..." refers background or methods in this paper

...Reduction to Fredholm integral equations The reduction of the previously obtained dual integral equations to the Fredholm integral equation is possible by the procedures in [46] or [47]....
[...]
...Next, an auxiliary functionψ is defined and to satisfy (38), with the consideration in [46] or some calculation abbreviated for brevity [47], the following formulation is considered:...
[...]