Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems

Chue, Ching Hwei; Chen, Chung De

doi:10.1016/s0020-7683(02)00247-0

Cited by 46 publications

(30 citation statements)

References 23 publications

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“…Basically, the formulations of junction problems are similar to those of wedge problems, [10]. For completeness, we will list some important equations briefly here and derive the eigenequation from the continuity conditions along the interfaces.…”

Section: Basic Formulationmentioning

confidence: 99%

“…The expressions for parameters u, v, w, U, K i and X i can be found in [10]. The coefficients l k ðk ¼ 1; 2; 3; 4Þ are the roots of the following characteristic equation:…”

Section: Basic Formulationmentioning

confidence: 99%

“…Here a ij , b ij and d ij are the reduced material constants and depend on the poling direction g, [10].…”

Section: Basic Formulationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Basic Formulationmentioning

confidence: 99%

“…The expressions for parameters u, v, w, U, K i and X i can be found in [10]. The coefficients l k ðk ¼ 1; 2; 3; 4Þ are the roots of the following characteristic equation:…”

Section: Basic Formulationmentioning

confidence: 99%

“…Here a ij , b ij and d ij are the reduced material constants and depend on the poling direction g, [10].…”

Section: Basic Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The stress singularities at the apex of composite piezoelectric junctions

Weng

Chue

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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“…Theocaris introduced the complex formulation to solve the singularity order in plane elasticity [2]. After these pioneers' efforts, the problems related to stress singularities were extended to anisotropic materials [3], muli-material wedges [4] and functional materails [5].…”

Section: Introductionmentioning

confidence: 99%

Investigations of Bending Singularity Orders in a V-notched Composite Laminate Plate Based on the Ressiner-Mindlin Theory

Chen

2018

MATEC Web Conf.

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Abstract. In this paper, the bending singularity at the apex of a V-notched composite laminate plate is investigated. The anisotropy of the laminate is modeled by the Stroh formalism. Based on the eigenfunction expansion method, the bending singularity orders can be determined by solving an eigenvalue problem numerically. The singularity orders depend on the plate angle, material orientation, material anisotropy and the laminate stacking sequence. The comparison cases show that the material orientation should avoid in order to reduce the bending singularity. The layers near the free surfaces have more significant effects on the singularity order. The findings presented in this paper are helpful in the design of the composite laminate with V-notch.

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Advanced Mechanics of Piezoelectricity

Qin

2013

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Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems

Cited by 46 publications

References 23 publications

The stress singularities at the apex of composite piezoelectric junctions

The stress singularities at the apex of composite piezoelectric junctions

Investigations of Bending Singularity Orders in a V-notched Composite Laminate Plate Based on the Ressiner-Mindlin Theory

Advanced Mechanics of Piezoelectricity

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