Concentration of electroelastic fields in a composite piezoceramic plate with a hole intersecting the interface of materials

A plane problem of electroelasticity is considered for an infinite compound plate with a hole located in both constituents of the plate. The corresponding boundary value problems is reduced to a system of singular integral equations of second kind, which is solved in numerical quadratures. Calculation results are presented that describe the concentration of electroelastic fields near the hole upon action at infinity of the vectors of mechanical stresses and electric field strength.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 359–366, May–June, 1999.     

Effect of shear compliance in bending and torsion on the stress concentration in a transversely isotropic plate with a hole whose edge is supported

The stress concentration in shear-compliant, transversely isotropic plates with a hole whose edge is supported has been investigated in bending and torsion. Two variants of the boundary conditions are examined. It is shown that the use of the classical Kirchhoff model may lead to a number of qualitative discrepancies.Mathematical Physics Branch, Institute of Mathematics, Academy of Sciences of the Ukrainian SSR. Translated from Mekhanika Polimerov, No. 3, pp. 458–463, May–June, 1975.     

Stress state of a composite shell with a sizable opening

The stress-strain state of a nonshallow cylindrical shell of a composite material is investigated. The shell is weakened by a circular hole and loaded with internal pressure. For solving the problem, the variational-difference method is used. The calculations are carried out for an orthotropic shell with a sizable hole, with account of the reduced shear stiffness of the material.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 49–56, January–February, 2005.     

Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

Ground state of electrons in a weakly doped narrow-band hubbard magnetic material

The thermodynamics of a low-doped narrow-band Hubbard magnetic material is described in the framework of a consistent perturbation theory using the diagram technique of the t-J model. Possible magnetic structures are investigated. Up to the linear approximation in the hole concentration, it is shown that the ground state of the electrons is ferromagnetic.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 2, pp. 311–323, November, 1995.     

Influence of geometric parameters on the stress concentration in an elastoplastic cylindrical shell

The elastoplastic stress-strain state of cylindrical shells weakened by a curvilinear (circular) hole is investigated. Numerical results are given for shells with a reinforced hole under the action of an internal pressure of specified intensity. The influence of the geometric parameters of the shell on the stress distribution in the concentration zone is investigated in the elastic and inelastic stages of deformation. The variation in flexure along the hole contour is given for linear and nonlinear problems, and the distribution of the maximum stress-concentration coefficients is also given for various geometric parameters.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 100–103, 1988.     

Stress analysis near holes in shells of revolution: Geometrically nonlinear problem

An approach is proposed to numerical analysis of the stress state of shells of revolution in the geometrically nonlinear setting. It is based on a combination of linearization and discrete orthogonalization methods. Stress concentration is analyzed for a flexible spherical shell with a central hole, depending on load intensity, hole size, and the boundary conditions on the contours in the precritical strain region.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 97–101, 1985.     

Problem of the infusion of a fluid in an elastic deformable medium

The problem of the infusion of a fluid in an elastic coal seam via a hole drilled from the daylight surface is solved. Analytical expressions that make it possible to investigate the effect of the stress—strain state, physicomechanical and collecting properties of the coal, and the rate of injection on the process of fluid infusion under prescribed conditions, are obtained.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 112–116, 1190.     

Action of a concentrated load on an elastic ring pressed into a circular hole in an anisotropic plate

A solution is obtained for the elastic equilibrium problem for an anisotropic plate with a circular hole into which is pressed a ring of arbitrary cross section symmetrical about the middle surface of the plate. Before deformation the outside radius of the ring differs from the radius of the hole in the plate by the amount of the permissible elastic displacements. A normal concentrated load is applied to the ring. The ring is analyzed in accordance with the theory of thin curved bars. A numerical example is given.I. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 6, pp. 1054–1059, November–December, 1973.     

Effect of gas seepage on stress-field redistribution in the vicinity of a hole

The effect of gas seepage on the stress-strain state of a coal seam is investigated. The problem of the degassing of coal seams with long holes is discussed. It is established that normal tensile stress components develop with the movement of gas in the vicinity of a hole. For certain ultimate tensile strengths of the coal, this reduces to failure of the walls of the hole, and to the development of dynamic phenomena.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 115–119, 1987.     

Flexure of thin inhomogeneous isotropic plates

The problem of the flexure of an inhomogeneous plate with a hole may be reduced, by the small-parameter method, to the solution of a series of problems for a homogeneous plate with a hole. These problems are solved using classical complex-potential methods. For an infinite plate with a circular hole, the results of numerical calculations are given; from these results, it follows that inhomogeneity of the material has a considerable influence on the stress.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 43–49, 1987.     

Diffraction of an acoustic pulse on a soft sphere with a hole

We study the axisymmetric problem of scattering of an acoustic pulse on a soft spherical shell with a hole. We analyze the structures of the echo-signals in the distant field for resonators with various openings.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 78–81.     

Stress distribution near a reinforced elliptical hole in a spherical shell at the elastoplastic stage of deformation

On the basis of Lagrange's variational equation the authors obtained nonlinear resolvent equations and coefficients taking into account the effect of a reinforcing element (a rod) on the state of stress and strain of a spherical shell weakened by a curvilinear (elliptical) hole. The article explains the method of numerical investigation of the inelastic state of the shell based on the application of the variational difference method in combination with the method of elastic solutions. The inelastic state of a shell with a reinforced hole was numerically investigated.Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 80–83, 1990.     

Evaluating the strength of plates of composite laminates in the region of a bolted joint

Conclusions The proposed efficient method of calculation of the SSS and the strength of CLM plates in the region of a loaded hole makes it possible, comparing with the FEM, to reduce the computing time, the amount of initial data, and the amount of memory that is necessary. The shown calculated and experimental data indicate that the proposed method can be used for calculation of the strength and type of failure on the stage of designing mechanical joints made of the CLM.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 877–883, September–October, 1990.We thank V. V. Dolin for his assistance in performing the experiment.     

Stress relaxation in a polymer disk

The stress relaxation in a polymer disk with a central hole, into which a rigid metal rod is press-fitted, is considered. The progressive redistribution of the stresses in the disk has been observed by a photoelastic method. In the theoretical solution of the problem the relaxation properties of the polymer are taken into account by means of a generalized nonlinear Maxwell equation with two terms of the relaxation spectrum. It is shown that the linear, as distinct from the nonlinear, theory is not capable of conveying the characteristics of the stress relaxation process in a rigid polymer disk.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1064–1070, November–December, 1971.     

State of stress of an anisotropic plate with a closed rod pressed into a curvilinear hole in it

A method is proposed for solving the problem of elastic equilibrium in the case of an anisotropic plate with a closed rod pressed into a curvilinear hole in it (or stretched over an anisotropic disk). This method is based on representing the boundary conditions in the form of contour integrals of an arbitrary function holomorphic within the region of that plate. The normal magnitude of the jump of the displacement vector at the contact line is given as the function of the arc. Friction at the contact line is assumed negligible. The stress-strain state of the rod (ring) is described by the equations in the theory of thin curvilinear beams.I. V. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 2, pp. 304–309, March–April, 1976.     

Geometrically nonlinear dilation of an orthotropic plane with an elliptical hole

In a geometrically nonlinear formulation we obtain expressions for the stresses and displacements on the edge of an elliptical hole in an orthotropic plane dilated by a strain at infinity in the direction of the principal axes of anisotropy. We exhibit the dependence of the concentration of stresses on the magnitude of the load acting on the plane. We prove that the stresses are finite at the ends of the crack and we compute their values. We confirm the need to take account of the geometric nonlinearity of the problem for low-modulus orthotropic materials.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 90–96.     

Indefinite metric and scattering by a domain with a small hole

For the problem of plane waves scattered by a domain with a small hole, we suggest a model based on the theory of self-adjoint extensions of symmetric operators in a space with indefinite metric. For two-dimensional problems of scattering on a line with a hole and on a semi-ellipse connected by a hole with a half-plane, we justify the choice of extension that guarantees the coincidence of the model solution with the solution of the actual problem in the far zone with a high degree of accuracy.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 837–850, December, 1995.The authors are grateful to B. S. Pavlov and L. M. Grigoryan for useful discussion.The work was partially supported by the State Commission on Higher Education of the Russian Federation under grant No. 94-2.7-1067.     

Limiting equilibrium of a plane with a circular hole

The elastoplastic state of a compressible isotropic plane with a circular hole is studied by the method of a small parameter. An unknown boundary separating the domain of limiting equilibrium and the elastic domain is determined. We construct the complex Kolosov-Muskhelishvili functions that describe the elastic state of a plane and compare these with the solutions of Galin's problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 980–981. July, 1993.     

Bending of a cantilevered glass-reinforced plastic cylindrical shell weakened by a circular opening

The stress concentration is investigated in the neighborhood of a circular opening in a cantilevered glass-reinforced plastic cylindrical shell with a concentrated load at the free end. The problem is solved by the Bubnov method using a Ural-2 computer. The theoretical results have been checked experimentally on glass-reinforced plastic shells.All-Union Correspondence Polytechnic Institute, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 152–157, January–February, 1970.