Unloading near a shear band: a free boundary problem for the wave equation

ABSTRACT

For solutions on unbounded domains of boundary value problems for a class of quasilinear elliptic equations which are not uniformly elliptic, we prove that the solutions have the same bounds as those of the boundary data.     

Combined compression and shear of a plasticoviscous film in the case of two-dimensional deformation

A method is proposed for calculating the load-carrying capacity of a lubricant having known rheological characteristics under the action of normal and tangential loads. Equations are given for determining the approach time of the pressure surfaces, and it is shown that the simultaneous action of normal and tangential loads leads to a decrease in the load-carrying capacity of the lubricant layer, which increases the probability of its destruction.Mekhanika Polimerov, Vol. 2, No. 2, pp. 269–277, 1966     

The influence of anisotropy on the stress concentration near a hole in a conical shell

On the basis of the variational method we discuss an approach to the computation of the stress-strain state of a conical shell made of a composite material and weakened by a hole. For a glass-plastic shell with a round unreinforced hole we study the influence of the variation of an interlayer shear and orthotropy on the stress concentration. Two tables. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 63–67, 1991.     

The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane

For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow.     

Problems of the concentration of elastic stresses near defects in spherically multilayered media

A spherically multilayered medium, whose elastic parameters change abruptly on the spherical surfaces, with defects in the form of cracks or thin rigid inclusions, is considered. The method of solving problems of the stress concentration near such defects is based on the introduction of linear combinations of the displacements and stresses as the fundamental unknowns. This enables the difficulties related to the presence of an arbitrary number of layers to be effectively overcome. The method is described initially for an unbounded elastic medium and defects of spherical form, situated on the surfaces where the elastic parameters change (interphase defects) and a way of extending this to the case of an elastic medium of finite dimensions, defects of other forms and not situated on these surfaces, is indicated. The method is described in detail as it applies to the case of a two-layer medium with an interphase crack when a torsion centre at the origin of coordinates acts on the medium. The problem is reduced to an integral equation, an effective method of solving it is given, and a formula is obtained for the stress intensity factor.     

Axial Couette flow of a generalized Oldroyd-B fluid due to a longitudinal time-dependent shear stress

Abstract

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylinder are determined by means of Hankel and Laplace transforms. The solutions that have been obtained, written in terms of the generalized G-functions, satisfy all imposed initial and boundary conditions. The similar solutions for generalized Maxwell fluids as well as those for ordinary fluids are obtained as limiting cases of our general solutions.     

On the bending of plates with transverse shear deformation and mixed periodic boundary conditions

The method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.     

On the regularity of a free boundary near contact points with a fixed boundary

We investigate the regularity of a free boundary near contact points with a fixed boundary, with C1,1 boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C¹ up to the fixed boundary. We will also construct some examples of irregular free boundaries.     

The velocity and shear stress functions of the Falkner-Skan equation arising in boundary layer theory

New compactness results on the velocity functions and shear stress functions of the well-known Falkner-Skan equation are obtained. The methodology is to utilize the equivalence between the Falkner-Skan equation and a singular integral equation established recently by Lan and Yang.     

Wavelength selection in convection near a lateral boundary

^** Corresponding author. This paper considers the way in which a lateral boundary restrictsthe wavelength of convective rolls parallel to the boundary.Unlike previous theories of wave number selection, the presentwork allows for perpendicular cross rolls adjacent to the boundary,the existence of which is indicated by stability considerations.The present theory also incorporates forcing at the boundary,equivalent to a wall that is imperfectly insulated, as in manyexperimental investigations of Rayleigh–Bénardconvection. The results are based on weakly non-linear solutionsof amplitude equations derived from the Swift–Hohenbergmodel and are compared with numerical solutions of the fullnon-linear Swift–Hohenberg equation.     

The behavior of the free boundary near the fixed boundary for a minimization problem

We show that the free boundary ∂{u > 0}, arising from the minimizer(s) u, of the functional

Periodic shear deformation of a curing epoxy composition

The curing of an epoxy resin with amines is investigated in relation to the changes in the viscoelastic shear characteristics. The effect of the shear deformation amplitude on the curing kinetics is considered.Presented at the Symposium on Polymer Rheology, Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow, May, 1970.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 301–306, March–April, 1971.     

Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

This paper studies the electro-mechanical shear buckling analysis of piezoelectric nanoplate using modified couple stress theory with various boundary conditions.In order to be taken electric effects into account, an external electric voltage is applied on the piezoelectric nanoplate. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using Hamilton's principle and nonlinear strains of Von-Karman. The modified couple stress theory has been applied to considering small scale effects. An analytical approach was developing to obtain exact results with various boundary conditions. After all, results have been presented by change in some parameters, such as; aspect ratio, effect of various boundary conditions, electric voltage and length scale parameter influences. At the end, results showed that the effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant.