Mixed Boundary Value Problems of Thermopiezoelectricity for Solids with Interior Cracks
Mixed Boundary Value Problems of Thermopiezoelectricity for Solids with Interior Cracks
复制标题
内部裂纹固体热压电混合边值问题
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
D. Natroshvili
中科院分区：
文献类型：
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作者：
T. Buchukuri;O. Chkadua;D. Natroshvili
摘要。研究了具有内裂纹的均匀各向异性固体的热电（热电弹性）混合边值问题解的渐近性质。利用有边界流形上伪微分方程的势方法和理论，证明了其解的存在唯一性。分析了裂纹边缘附近和边界条件类型发生变化的曲线附近的力学场、热场和电场的奇异性和渐近行为。特别地，对于一些重要的各向异性介质，我们导出了相应的应力奇异指数的显式表达式，并证明了它们与材料参数的依赖关系。与所谓的振荡奇点有关的问题也作了详细的讨论。
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.