The action of a concentrated force and a concentrated electric charge in an infinite transversally isotropic piezoceramic medium

An explicit solution of the problem of electroelasticity is constructed for a transversally isotropic medium under the action of a concentrated force and a concentrated electric charge. The cases where the force acts along the anisotropy axis and along the isotropy axis are considered. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 80–87, April, 2000.     

Homogenization of the signorini boundary-value problem in a thick plane junction

We consider a mixed boundary-value problem for the Poisson equation in a plane thick junction Ω_ε that is the union of a domain Ω₀ and a large number of ε-periodically located thin rods. The nonuniform Signorini conditions are given on the vertical sides of the thin rods. The asymptotic analysis of this problem is made as ε → 0, i.e., in the case where the number of thin rods infinitely increases and their thickness tends to zero. With the help of the integral identity method, we prove the convergence theorem and show that the nonuniform Signorini conditions are transformed (as ε → 0) into the limiting variational inequalities in the domain that is filled up with thin rods when passing to the limit. The existence and uniqueness of a solution to this nonstandard limit problem are established. The convergence of the energy integrals is proved as well. Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 44–58, January–March, 2009.     

Solution of the plane Hertz problem

The paper considers the problem of onesided frictionless compression of plane elastic bodies that are initially in contact with each other at a point. The first terms of an asymptotic solution of the problem are constructed by the method of joined asymptotic expansions. Determination of the approach of the bodies as a function of the pressing force reduces to calculating socalled of local compliance. The problems of contact of an elastic ring and elastic circular disks with punches and an elastic disk compressed between two elastic strips are considered. An asymptotic model for the quasistatic collision of plane elastic bodies is proposed.     

The stress state of a viscoelastic orthotropic half-plane loaded with a concentrated force

The operator continued-fraction method is used to solve the problem on the stress state of a viscoelastic orthotropic half-plane loaded at a momentt=0 with a force normal to the boundary of the half-plane. The stress field in the half-plane is determined based on the Volterra principle and the solution of the corresponding elastic problem. The influence of the rheological parameters on the stress state of the half-plane is shown by an example of a specific material. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 124–130, February, 2000.     

On the dynamic behaviour of an elastically supported beam of infinite length, loaded by a concentrated force

Summary An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by =0 for and =K=const. for ; the second one by =0 for 0 > > , given function of for 0 ; the third one applies to problems in which, during the period of impact, itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties.     

Solution of a problem concerning the motion of viscoelastic materials

We give a general solution of a problem involving plane-parallel shearing motion of a Maxwell body in a plastometer subject to a quasistatic concentrated interaction. In our solution we employ physicomathematical modelling of the microstructure and creep processes in the distributed mass of viscoelastic materials.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 172–175, November–December, 1974.     

The Saint-Venant problem of plane bar under an axial force

I.PrefaceAsweknow,theSaint-Venanttheoryisawell-knownanduniversallyacceptedtheory.Butasoneofthegeneraltheoriesofelasticmechanics,itisnotprovedperfectely,althoughitistestedbyexperiments.Infact,onlyforthesimplestproblemofelasticity,itisnoteasytofindanalytics…     

Solution of the problem of a concentrated torque on a semi-space by similarity transformations

Similarity transformations are constructed and used to obtain an exact solution for the axisymmetric boundary value problem of a homogeneous isotropic elastic semi-space subjected to a concentrated torque normal to its surface.     

Determining the material constant in the equilibrium problem for an infinite elastic plane weakened by a circular hole

The averaging method is used to determine the material functions of the linear Cosserat theory of elasticity. The proposed method is used to find the material constant in the equilibrium problem for an infinite plane weakened by a circular hole.     

A moving punch on an infinite viscoelastic layer

Summary The problem of a rigid punch pressed against and moved on the surface of an elastic or viscoelastic layer is studied. It is shown that the governing equations reduce to the same integral equation for the elastic contact problem. Two particular motions of the punch are considered. In the first case the punch moves at a constant speed along a straight line on the surface of a viscoelastic layer. In the second case the punch moves at a constant speed along a circular path. Finally, the special case of a punch moving on a layer of a standard linear viscoelastic solid is studied. The equation is identical to a punch of modified shape pressed on an elastic layer.The work presented here was supported by the National Science Foundation under Grant GK 35163 with the University of Illinois.With 1 figure     

The lifting force action on a contour in a plane homogeneous vortex flow of an incompressible ideal fluid

The plane problem of homogeneous vortex flows of an incompressible inviscid fluid around a contour is considered. A method is developed for contours having a center or an axis of symmetry for calculating the lifting force acting on the contour which reduces the problem of determining the lifting force to an ordinary problem of a potential flow of a fluid around the given contour.