On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space

The paper establishes the relationship between the static contact problems of elasticity and electroelasticity (in the absence of friction) for a transversely isotropic half-space whose surface is the isotropy plane. This makes it possible to avoid solving the electroelastic problem by finding all the characteristics of electroelastic contact from known cases of purely elastic interaction. Moreover, the electroelastic state of the half-space can be fully described using a known harmonic function, which is a solution of the purely elastic problem. The approach is exemplified by solving contact problems of electroelasticity for flat, elliptic, two circular, conical, and paraboloidal (circular and elliptic in plan) punches __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 69–84, November 2006.     

Asymptotic models of contact interaction among elliptic punches on a semiclassical foundation

Consideration is given to the contact without friction among an arbitrary number of elliptic punches or punches in the form of an elliptic paraboloid and an elastic half-space with Young's modulus as a power-law function of the distance from the edge. Asymptotic models of contact interaction are designed assuming that the distance between punches is large compared with their dimensions __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 78–96, January 2006.     

Nonstationary axisymmetric problem of electroelasticity for a piezoceramic cylinder with circular polarization

This paper considers the problem of the propagation of forced electroelastic axisymmetric torsional waves in a hollow piezoceramic cylinder of finite dimensions, whose curvilinear electroded surfaces are subjected to shear stresses or an electrical potential. A new closed solution is constructed by expansion in vector eigenfunctions using the structural algorithm of finite integral transforms, which makes it possible to determine vibration eigenfrequencies, the stress-strain state of the element, and the potential and intensity of the induced electrical field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 12–21, January–February, 2009.     

Thermoelastic State of a Transversely Isotropic Layer between Two Annular Punches

A technique is developed to solve contact problems for annular punches interacting with a transversely isotropic layer. The contact problem for two heated annular punches interacting with a layer is solved. The formulas for the contact stresses under the punches are derived, and the effect of the shape of the punches on the magnitude and distribution of these stresses is analyzed     

An approach to the contact problem for a circular punch on an elastic foundation

Rektorys’ approach is used in implementing the Ritz method to solve the contact problem for a circular punch on an elastic foundation of general form __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 65–71, April 2008.     

Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion

The paper establishes a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic piezoceramic medium and opened (without friction) by rigid inclusions and the solutions for cracks in a purely elastic medium. This makes it possible to calculate the stress intensity factor (SIF) for cracks in an electroelastic medium from the SIF for an elastic isotropic material, without the need to solve the electroelastic problem. The use of the approach is exemplified by a penny-shaped crack opened by either a disk-shaped rigid inclusion of constant thickness or a rigid oblate spheroidal inclusion in an electroelastic medium __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 47–60, July 2008.     

Uniqueness for the solutions of elastic thin plates and shallow shells as well as their contact problem with half space

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｇｏｖｅｒｎｉｎｇｅｑｕａｔｉｏｎｓｆｏｒａｎｉｎｖｅｒｔｅｄｅｌａｓｔｉｃｔｈｉｎｓｈａｌｌｏｗｓｈｅｌｌｏｎｅｌａｓｔｉｃｈａｆｓｐａｃｅｉｎｓｔａｔｉｃｂｅｎｄｉｎｇａｒｅ[1]4-Ｅｉｈｉ2ｋｗ=02=2/ｘ2 2/ｙ2,2ｋ=ｋｙ(2/ｘ2) ｋｘ(2/ｙ2),(1)Ｄｉ4ｗ 2ｋ=ｑ-ｐ,(2)ｗ(ｘ,ｙ)=λｅ 2Ｇｅ4πＧｅ(λｅ Ｇｅ)∫∫ｓｐ(ξ,η)ｄξｄη(ｘ-ξ)2 (ｙ-η)2,(3)ｗｈｅｒｅｉｎＥｑｓ.(1),(2)ａｎｄ(3),ｗ(ｘ,ｙ)ｉｓｔｈｅｄｅｆｌｅｃｔｉｏｎｏｆｔｈｅｓｈｅｌｌ,(ｘ,ｙ)ｉｓｔｈｅｍ…     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

Determination of Interlaminar Stresses in Bending Problems for a Stack of Transversely Isotropic Plates

A mechanical and mathematical bending model for a stack of transversely isotropic plates is developed. The resolving equations for deflections and tangential displacements are supplemented with a system of differential equations for normal and tangential contact stresses. It is demonstrated that for stacks consisting of an arbitrary number of identical plates with no friction between them, the initial system of equations for contact stresses can be reduced to Helmholtz equations. This transition allows obtaining the complete eigenvalue spectrum for the Laplasian of the problem and, in special cases, eigenfunctions. They are Krylov functions when bending is cylindrical and Bessel functions when bending is axisymmetric     

Nonstationary indentation of a blunt rigid body into an elastic layer: An axisymmetric problem

The nonstationary indentation of a blunt rigid body into an elastic layer is studied. The general formulation of the problem includes different boundary conditions in the contact area and on the free surface of the layer. The simplified nonmixed problem that arises at the early stage of interaction and allows obtaining approximate results for later times is solved exactly. The solution obtained is compared with that for the plane case __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 35–46, July 2008.     

Nonstationary indentation of a rigid blunt indenter into an elastic layer: A plane problem

The nonstationary indentation of a rigid blunt indenter into an elastic layer is studied. An approach to solving a mixed initial-boundary-value problem with an unknown moving boundary is developed. The problem is reduced to an infinite system of integral equations and the equation of motion of the indenter. The system is solved numerically. The analytical solution of the nonmixed problem is found for the initial stage of the indentation process __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 55–65, March 2008.     

A mixed problem of plane elasticity for a domain with partially unknown boundary

The paper addresses a problem of plane elasticity for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides. The neighborhoods of the vertices of the inner boundary are unknown equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center. It is assumed that this elastic body is inserted into a hole of a rigid body, with the hole boundary coinciding with the outer boundary of the elastic body. Absolutely smooth rigid punches with rectilinear bases are pressed into all the rectilinear sections of the inner polygonal boundary of the elastic body. There is no friction between the elastic and rigid bodies. The unknown arcs are free from external stresses. Complex variable theory is used to determine the unknown arcs and the stress state of the elastic body __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 110–118, March 2006.