Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity

Podil'chuk, Yu. N.; Myasoedova, I. G.

doi:10.1007/s10778-005-0034-3

Cited by 10 publications

(2 citation statements)

References 7 publications

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“…As a result we obtain Comparing the obtained expressions (13) with (5), we may conclude that the multiplier at n i n j is identical in all expressions σ * ij | S (i = j) in (13). We now represent the stress state in the medium with cavity as a superposition of states:…”

Section: Solution Of the Inverse Thermo-elasticity Problemmentioning

confidence: 82%

“…Inverse thermo-elasticity problems for an isotropic matrix with an elastic isotropic or transversally isotropic inclusion under three-axes tension and uniform heating of matrix and inclusion were studied in [10,11]. We note that some direct problems for ellipsoidal cavities and inclusions in anisotropic media, which could be used in some cases for solving inverse problems, were considered in [12][13][14][15], [16,Chapt. 4].…”

Section: Introductionmentioning

confidence: 99%

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On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape

Kirilyuk

Levchuk

2007

J Eng Math

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The static inverse thermoelastic problem for an infinite elastic isotropic medium containing a cavity of unknown shape, under three-axes tension and given constant values of the pressure and the temperature on the cavity surface, is considered. The shape of a cavity is sought subject to the condition that certain stress components are uniform on the cavity surface. It is shown that ellipsoidal shapes furnish a solution of this inverse thermo-elasticity problem. Nonlinear equations for determining the geometric cavity parameters, which lead to an equal-stress state along the cavity surface, are obtained. Results of other authors for force loading only are obtained as special cases. Numerical investigations have been carried out and correlations between values of the force and temperature loadings and geometrical parameters for an equal-stress cavity surface are studied. The stress values on the equal-stress cavity surface under force and temperature loadings are investigated.

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Section: Solution Of the Inverse Thermo-elasticity Problemmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape

Kirilyuk

Levchuk

2007

J Eng Math

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Thermoelectroelastic state of a piezoceramic body with a spheroidal cavity in a uniform heat flow

Podil'chuk

Kovalenko

2005

Int Appl Mech

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An exact solution is obtained to the three-dimensional problem of thermoelectroelasticity for a piezoceramic body with a spheroidal cavity. The solutions of static thermoelectroelastic problems are represented in terms of harmonic functions. Far from the cavity, the body is in a uniform heat flow perpendicular to the axis of symmetry of the cavity Keywords: thermoelectroelasticity, statics, stress state, piezoceramic body, spheroidal cavity, uniform heat flowResults from stress analysis of piezoceramic bodies under mechanical and thermal loads are presented in [5-9, etc.]. The paper [5] gives a closed-form solution for bodies with an elliptic cavity or a crack subjected at infinity to a constant electroelastic field or point forces and charges. The authors of [6, 7] studied the vibrations and dissipative heating of thickness-polarized circular piezoceramic plates with nonuniformly electroded surfaces and of partially depolarized piezoceramic sphere under harmonic loading. The three-dimensional problem of electroelasticity for transversely isotropic piezoceramic bodies with a spheroidal cavity was solved in [9].Here we will find the exact solution to the static problem of thermoelectroelasticity for a piezoceramic body with a spheroidal cavity. The axis of symmetry of the spheroid coincides with the axis of anisotropy of the body. Far from the cavity, the body is in a uniform heat flow perpendicular to the cavity's axis of symmetry.

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Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

Kirilyuk

2006

Int Appl Mech

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The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear Keywords: piezoelectricity, plane crack, antisymmetric load, elliptic crack, stress intensity factor Introduction. Various transducers and sensors are often made of piezoelectric ceramic materials (where the mechanical and electric fields are coupled) that are highly brittle. This necessitates a detailed study of the concentration of mechanical and electric fields in piezoceramic bodies with imperfections such as cavities, inclusions, and cracks. However, solving three-dimensional problems of electroelasticity involves significant mathematical difficulties, because the original equations of electrostressed state constitute a complicated system of partial differential equations [1,4]. Plane problems of electroelasticity and magnetoelasticity were studied more fully in [2, 13, 15, 20, 21, etc.]. These studies address both the two-dimensional electroelastic state near single cavities, inclusions, and cracks and the interaction of concentrators of electric and mechanical fields. Three-dimensional problems of electroelasticity for an infinite medium with cavities, inclusions, and cracks were solved in [5-7, 10, 16, 19]. The papers [5,11,19] propose approaches to find general solutions to coupled equations of electroelasticity for a transversely isotropic body. Exact solutions to problems of electroelasticity for spheroidal cavities and inclusions were found in [6,16]. The electrostressed state and stress intensity factors (SIFs) of an infinite medium with penny-shaped and elliptic cracks were analyzed in [1, 10, 18] and [7], respectively.

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Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity

Cited by 10 publications

References 7 publications

On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape

On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape

Thermoelectroelastic state of a piezoceramic body with a spheroidal cavity in a uniform heat flow

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

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