Mixed Boundary Value Problems of Thermopiezoelectricity for Solids with Interior Cracks |
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Authors: | T Buchukuri O Chkadua D Natroshvili |
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Institution: | (1) A. Razmadze Mathematical Institute, 1 M. Aleksidze st., Tbilisi, 0193, Georgia;(2) Georgian Technical University, 77 M. Kostava st., Tbilisi, 0175, Georgia |
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Abstract: | We investigate asymptotic properties of solutions to mixed boundary value problems of thermopiezoelectricity (thermoelectroelasticity)
for homogeneous anisotropic solids with interior cracks. Using the potential methods and theory of pseudodifferential equations
on manifolds with boundary we prove the existence and uniqueness of solutions. The singularities and asymptotic behaviour
of the mechanical, thermal and electric fields are analysed near the crack edges and near the curves, where the types of boundary
conditions change. In particular, for some important classes of anisotropic media we derive explicit expressions for the corresponding
stress singularity exponents and demonstrate their dependence on the material parameters. The questions related to the so
called oscillating singularities are treated in detail as well.
This research was supported by the Georgian National Science Foundation grant GNSF/ST07/3-170 and by the German Research Foundation
grant DFG 436 GEO113/8/0-1. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 35J55 Secondary 74F05 74F15 74B05 |
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