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The electroelastic problem of the stress state of an electroelastic transversely isotropic medium in which a rigid disk-shaped inclusion is displaced under a load non-centrally applied to its surface is solved exactly. Closed analytical expressions for displacements and stress distributions in the piezoelectric material below the inclusion are derived. The solutions of the static electroelastic equations for a transversely isotropic body represented in terms of harmonic functions are used. The problem is reduced to pair integral equations. Expressions for the stress state of a purely elastic transversely isotropic material with a disk-shaped inclusion under non-central load on its surface the follow from the obtained analytical formulas as partial cases. The effect of the coupling of the mechanical and electric fields on the stress distribution below the rigid inclusion under non-central loading is studied numerically. [ABSTRACT FROM AUTHOR]

Based on a rigorous mathematical statement that takes into account the coupling of the mechanical and electric fields, the problem of the compression of two electroelastic transversely isotropic half-spaces is solved. One of the half-spaces contains an inclined near-surface notch of elliptical cross-section. The analytical solution of the problem is found by representing the solution of the static equations of electroelasticity in terms of harmonic functions and by reducing the boundary-value problem to an integro-differential equation with an unknown domain of integration. As a partial case, the parameters of the contact of two elastic transversely isotropic half-spaces (if one of them has a notch of elliptical cross-section), as well as the parameters of the contact interaction of two electroelastic half-spaces, one of which contains a an axisymmetric notch, are obtained from the analytical expressions. Numerical results are obtained. The effect of the electroelastic properties of the half-spaces, the geometrical parameters of the notch, and loading on the contact interaction as well as the closure of the gap between the bodies is studied. [ABSTRACT FROM AUTHOR]

This paper is a study into the interaction of two triaxial ellipsoidal cavities whose surfaces are under different pressures with an elliptic crack in an infinite elastic medium. The stress state in the elastic space is represented by a superposition of perturbed states due to the presence and interaction of the cavities and the crack. The exact solution of the problem is constructed by using a modified method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for the elliptic crack. A numerical analysis is carried out to find how the geometry of the cavities and the crack, the distance between them, and the pressure on their surfaces affect the stress intensity factors [ABSTRACT FROM AUTHOR]

The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed [ABSTRACT FROM AUTHOR]