Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks
type: Item
instance of: scholarly article
title: Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks
zbMATH Open document ID: 1183.35263
published in: Integral Equations and Operator Theory
publication date: 2009-11-13T00:00:00Z
review text: The paper is devoted to the three-dimensional mixed type boundary value problems arising in the theory of thermopiezoelectricity (thermoelectroelasticity) for homogeneous anisotropic solids with interior cracks. Using the potential method and theory of pseudodifferential equations on manifolds with boundary, the existence and uniqueness of a solution of a boundary value problem for the pseudo-oscillation equations with the crack conditions and the mixed boundary conditions is proved. Asymptotic expansion formulas of solutions near the singularity curves are derived. The qualitative and quantitative properties of dominant singularity exponents of physical fields are investigated in detail. It is shown that these exponents can be calculated efficiently with the help of the symbol matrices of the corresponding pseudodifferential operators. Particular examples considered in the paper show that the stress singularity exponents essentially depend on the material parameters.
reviewed by: G. Jaiani
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 5633111
zbMATH Keywords: Thermoelasticity
zbMATH Keywords: piezoelectricity
zbMATH Keywords: thermopiezoelectricity
zbMATH Keywords: mixed boundary value problems
zbMATH Keywords: pseododifferential equations
zbMATH Keywords: potential methods
author: Tengiz Buchukuri
author: O. Chkadua
author: D. Natroshvili
MaRDI profile type: Publication
full work available at URL: s00020-009-1694-x
OpenAlex ID: W2007530234
DOI: 10.1007/S00020-009-1694-X
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description: scientific article; zbMATH DE number 5633111