The stressed state of a transversally isotropic medium with a spheroidal inclusion under nonideal mechanical contact

We study the problem of the stressed state of a transversally isotropic medium containing a foreign inclusion in the form of a prolate spheroid under an arbitrary homogeneous stress field at infinity. On the “medium-inclusion” interface there is slipping without flaking. The stressed state is constructed in the medium and in the inclusion using the exterior and interior problems for a prolate spheroid on the basis of potential functions. The solution of the problem is reduced to studying infinite systems of linear algebraic equations. The results of numerical studies are shown as graphs that describe the stress distribution in both the transversally isotropic medium and in the inclusion under various boundary conditions. Four figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 15–26.     

Stressed state of an anisotropic body with elliptical holes, elastic inclusions, and cracks

A method is proposed for studying the two-dimensional stressed state of a multiply connected anisotropic body with cavities and elastic and rigid inclusions, as well as planar cracks and rigid laminar inclusions. Generalized complex potentials, conformal mapping, and the method of least squares are used. The problem is reduced to solving a system of linear algebraic equations. Formulas are given for finding the stress intensity factors in the case of cracks and laminar inclusions. For an anisotropic plate with a single elliptical hole or a crack and an elastic (rigid) inclusion, some numerical results are presented from a study of the effect of the rigidity of the inclusion and the closeness of the contours to one another on the distribution of stresses and the stress intensity factor. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 175–187, 1999.     

The indentation of two rigid stamps into an elastic sphere with a spheroidal inclusion

On the basis of the expansion formulas of the vector solutions of the Lamé equations in spherical coordinates with respect to the solutions of the Lamé equations in oblate spheroidal coordinates and on the basis of their inverse formulas, one solves the problem of the compression of an elastic ball with an absolutely rigid inclusion in the form of an oblate spheroid. The problem is reduced to an infinite system of linear algebraic equations of the second kind with a completely continuous operator in ₂. Results of the numerical solution of the infinite system are given and the obtained results are analyzed.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 9–13, 1989.     

Stressed state of elastic plane with cavities

An algorithm for the numerical solution of the problem of defining the stressed state of a loaded plane with cavities of arbitrary configuration is given. A system of singular integral equations is given, which is obtained by using displacement potentials, is quantizied by the method of discrete singularities and finite differences. Existence and uniqueness conditions for solutions are formulated. The algorithm is debugged on a test example and is applied to a study of interrelation of elliptic cavities when the distance between them decreases.Translated from Dinamicheskie Sistemy, No. 7, pp. 8–13, 1988.     

Stressed state of a rock mass around a working with a relief cavity

The stressed state of a rock mass in the vicinity of a preparatory working protected by a relief cavity is studied. A numerical study is made of the stress field and the relief zone, and the effect of length and slope of a slot on formation of the relief zone is clarified.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 31–36, 1989.     

Stressed state near cracks in elastic media

A modification of the known nonlinear Barenblatt-Leonov-Panasyuk model of cracks is given, which allows us to obtain a continuous distribution of tensions near cracks in conditions of finite deformations and smooth closings of their boundaries. Functional relations of formation and increase of cracks are given, which assume their experimental checking together with a determination of quantitative characteristics that belong to the model of parameters.Translated from Dinamicheskie Sistemy, No. 7, pp. 3–7, 1988.     

Electroelastic state of an inhomogeneous piezoceramic layer under symmetric loading

A procedure for solving three-dimensional mixed symmetric problems of electroelasticity theory for a piezoceramic layer with an inclusion, which is weakened with a through hole, is proposed. The boundary-value problem is reduced to a system of 12k (k = 1, 2, …) integrodifferential equations. Expressions for stresses characterizing the stress state of the inhomogeneous layer are found. Calculation results for characteristic stresses are presented.     

The thermally stressed state of a half-space with a cylindrical foreign inclusion

We propose a method of determining the thermally stressed state of semibounded bodies containing a defect in the form of a cylindrical foreign inclusion. We give the results of numerical study of the thermal stresses as functions of the geometric parameters of the inclusion. Four figures. Bibliography: 4 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 41–45.     

Stressed state of an elastic plane weakened by a narrow slot with partly closed edges

An elastic plane weakened by a narrow rectilinear slot with rounded ends is considered. The plane is compressed by force P at angle a to the slot axis and with force P in the perpendicular direction. Central areas of the slot edges close under the action of compression. Their reaction in relation to the ratio of parameters of the problem has the nature of sticking together or Coulomb friction. The stress-strain state of the system described is studied.Translated from Dinamicheskie Sistemy, No. 4, pp. 25–33, 1985.     

Effect of the curvature at the corner of a rectangular inclusion on the state of stress of a piecewise homogeneous body subjected to longitudinal shear

Using the function theory, the article examines antiplane strain of an isotropic body with a rectangular isotropic elastic inclusion. The solution of the problem is reduced to a system of linear algebraic equations. The article presents a numerical analysis of the state of stress at the corner in dependence on the curvature at this point and on the elastic constants of the matrix and of the inclusion.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 69–71, 1988.     

Stressed state of an elastoplastic isotropic shell with a through crack with regard for material hardening

We have solved the problem of determining the stressed state of an elastoplastic isotropic shell of arbitrary curvature with a through crack with regard for material hardening. We have obtained a system of singular integral equations and solved it numerically by the method of mechanical quadratures. We have also studied the influence of material hardening on the general characteristics of the stressed state.     

Elastic state of a plate with a circular plug and a rectilinear thin elastic inclusion

There is considered the problem of the state of stress of an infinite elastic plane with a bonded circular plug and an arbitrarily located thin elastic inclusion under biaxial tension. Conditions of ideal mechanical contact are satisfied on the line separating the materials. By using the complex Kolosov — Muskhelishvili potentials, the problem is reduced to a system of integro-differential equations which is solved numerically by utilization of a mechanical quadrature method. A numerical analysis is given for the solution of the problem of the elastic equilibrium of a plane with a circular hole and an arbitrarily located thin inclusion.