Line force, charge and dislocation in angularly inhomogeneous anisotropic piezoelectric wedges and spaces

Chung, M. Y.; Ting, T. C. T.

doi:10.1080/01418619508244377

Cited by 15 publications

(7 citation statements)

References 4 publications

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“…This is the case analyzed by Ting (1996a) following a di erent procedure. Ting relates these kinds of solutions to a class of particular elastic spaces, the angularly inhomogeneous elastic spaces (Ting, 1989;Chung and Ting, 1995) in which a similar hypothesis is made about the structure of the applicable Hooke's law.…”

Section: Stress-angularly and Radially Inhomogeneous Anisotropic Elasmentioning

confidence: 96%

“…These problems have been generalized and included in the wider category of angularly inhomogeneous problems (Ting, 1989;Chung and Ting, 1995) in which the composite of wedges is subjected to a line dislocation and a line force at = 0, as illustrated in Fig. 6a.…”

Section: Stress-angularly and Radially Inhomogeneous Anisotropic Elasmentioning

confidence: 99%

“…These cylinders are said to possess shape intrinsic orthotropy since it is the boundary of the cylinder that establishes the possible directional variation of the elastic moduli. A second example was given by Ting (1989) and Chung and Ting (1995) who presented an exact solution for the case of an anisotropic half-space with elastic moduli dependent upon one coordinate, the angle Â, when the loads on the half-space are represented by a straight line of force. These kinds of problems were called angularly inhomogeneous problems by the authors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions

Fraldi

Cowin

2004

Journal of the Mechanics and Physics of Solids

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Section: Stress-angularly and Radially Inhomogeneous Anisotropic Elasmentioning

confidence: 96%

Section: Stress-angularly and Radially Inhomogeneous Anisotropic Elasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions

Fraldi

Cowin

2004

Journal of the Mechanics and Physics of Solids

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“…Papers [6][7] employed Stroh's formalism to solve the problems of a homogeneous anisotropic piezoelectric wedge and an angularly inhomogeneous piezoelectric wedge subjected to a line force, line charge and line dislocation applied at the apex. Paper [8] studied the singular behavior of the inplane electro-elastic field near the apex of piezoelectric wedges and junctions, with the polarization orientation of the piezoelectric medium arbitrary in the (x-y)-plane.…”

Section: Introductionmentioning

confidence: 99%

The stress singularities at the apex of composite piezoelectric junctions

Weng

Chue

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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The stress singularities at the apex of a piezoelectric-conductor, -composite, or -piezoelectric junction are investigated under generalized plane deformation in this paper. The influencing parameters on the stress singularity order are the wedge angles, material properties, graphite fiber orientation, and piezoelectric poling direction. The singularities of decoupled inplane and antiplane electromechanical field s are investigated when piezoelectric materials are polarized in the (x-y)-plane or along the z-axis. From the numerical results, the conditions of strongest and weakest singularity orders can be determined. IntroductionDue to their electromechanical coupling behavior, piezoelectric materials, such as PZT-4, PZT-5, etc, are widely used in smart structures and electronic devices. Because the materials are brittle, cracking may start at the apex of these junctions where stresses are unbounded.It is known that three-dimensional piezoelectric problems can be decoupled into inplane and antiplane electro-elastic fields when the poling direction of the material is in the (x-y)-plane or along the z-axis. An extention of Stroh's formalism, [2], to an eight-dimensional framework was presented in [1] and the problem of piezoelectric insulators under a line charge and a straight dislocation was solved. Paper [3] extended the Lekhnitskii formalism [4] in anisotropic elasticity to derive a general solution to the plane strain piezoelectric problem in terms of complex potentials, assuming that the piezoelectric material is polarized along the x-or y-axis. The same approach was used in [5] to solve piezoelectric problems under generalized plane deformations. Exact correspondences have been indicated between plane piezoelectricity and generalized plane strain in elasticity.Piezoelectric wedge problems have not been yet addressed extensively. Papers [6-7] employed Stroh's formalism to solve the problems of a homogeneous anisotropic piezoelectric wedge and an angularly inhomogeneous piezoelectric wedge subjected to a line force, line charge and line dislocation applied at the apex. Paper [8] studied the singular behavior of the inplane electro-elastic field near the apex of piezoelectric wedges and junctions, with the polarization orientation of the piezoelectric medium arbitrary in the (x-y)-plane. Paper [9] applied the Mellin transform to the antiplane electric-mechanical field of a piezoelectric bonded wedge subjected to a pair of concentrate shear forces and free charges. In this study, the generalized stress, strain and electrical displacement intensity factors were derived analytically as well as the singularity orders and angular functions expressed in the electro-mechanical field. The formulation of piezoelectric elasticity under generalized plane deformation was derived in [10] and applied to wedge problems, while four decoupled cases were discussed in detail. Later, in paper [11] explicit forms were derived for eigen-equations, which govern the antiplane stress singularities of a bi-material piezoelectric wedge.T...

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“…A very interesting problem in anisotropic inhomogeneous elastic materials [1][2][3][4][5][6][7][8][9][10][11] is that of cylinders subjected to pure tension and possessing cylindrical orthotropy, with a variation of material properties in the local normal direction to the family of curves of which the lateral boundary is a member [2]. In another interesting problem Chung and Ting [5] and Ting [6] gave the solution of an anisotropic half-space with the elastic modulus dependent upon one coordinate, the angle, θ , when the loads on the half-space are represented by a straight line of forces.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Bonded Elastic Wedges with Angular Moduli Variation

Theotokoglou¹,

Stampouloglou²

2008

AIP Conference Proceedings

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Elasto-plastic stress analysis of thick-walled FGM pipes AIP Conf.The strain dependence of the dynamic moduli of short fiber reinforced thermoplastic blends Abstract. In this paper the bond effect in a graded elastic wedge consisting of two radially bonded sub-wedges, is investigated in linear elasticity. The inhomogeneous anisotropic self similar bi-wedge loaded by a concentrated force at its apex is first studied analytically under plane strain or generalized plane stress conditions, using the self similarity property. Based on the decomposition of loading in each sub-wedge and on the continuity of displacements at the interface, the stress and displacement fields are determined. An application has been made in the case of the wedge of angle, ( ) 2 θ π = .

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Line force, charge and dislocation in angularly inhomogeneous anisotropic piezoelectric wedges and spaces

Cited by 15 publications

References 4 publications

Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions

Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions

The stress singularities at the apex of composite piezoelectric junctions

Analysis of Bonded Elastic Wedges with Angular Moduli Variation

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