Search

In the present paper we investigate three-dimensional dynamical mixed boundary-transmission problems for composed body consisting of two adjacent anisotropic elastic components having a common interface surface. The two contacting elastic components are subject to different mathematical models: Green–Lindsay’s model of generalized thermo-electro-magneto-elasticity in one component and Green–Lindsay’s model of generalized thermo-elasticity in the other one. We assume that the composed elastic structure under consideration contains an interfacial crack. We prove the uniqueness and existence theorems in appropriate function spaces. [ABSTRACT FROM AUTHOR]

We investigate the solvability of three-dimensional dynamical mixed boundary value problems of electro-magneto-elasticity theory for homogeneous anisotropic bodies with interior cracks. Using the Laplace transform technique, the potential method, and the theory of pseudodifferential equations, we prove the existence and uniqueness theorems and analyze asymptotic properties of solutions near the crack edges and near the lines where the different boundary conditions collide. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of mixed boundary-transmission problems for composed elastic structures consisting of two contacting anisotropic bodies occupying two threedimensional adjacent regions with a common contacting interface, being a proper part of their boundaries. It is assumed that the contacting elastic bodies are subject to different mathematical models. In particular, we consider Green-Lindsay's model of generalized thermo-electro-magnetoelasticity in one elastic component, while in the other one, we considered Gree Lindsay's model of generalized thermo-elasticity. The interaction of the thermo-mechanical and electro-magneticffelds in the composed piecewise elastic structure is described by the fully coupled systems of partial differential equations of pseudo-oscillations, obtained from the corresponding dynamical models by the Laplace transform. These systems are equipped with the appropriate mixed boundary-transmission conditions which cover the conditions arising in the case of interfacial cracks. Using the potential method and the theory of pseudodifferential equations on manifolds with a boundary, the uniqueness and existence theorems in suitable function spaces are proved, the regularity of solutions is analyzed and singularities of the corresponding thermo-mechanical and electro-magneticffelds near the interfacial crack edges are characterized. The explicit expressions for the stress singularity exponents are derived and it is shown that they depend essentially on the material parameters. A special class of composed elastic structures is considered, where the so-called oscillating stress singularities do not occur. [ABSTRACT FROM AUTHOR]