Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks
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.
scientific article; zbMATH DE number 5633111