Asymptotic Solution of a Harmonic Contact Problem for a Permeable Stamp on a Liquid Saturated Base

A plane harmonic problem of vertical vibrations of a rigid permeable stamp on a liquid saturated poroelastic base is considered. The equations of two-phase Biot media, which take into account inertial and viscous interactions of phases, are used. The asymptotic properties of the contact stress at low vibration frequencies are studied.     

Some Remarks Concerning a Boundary-Value Problem in Nonlinear Elastostatics

The paper is concerned with solvability of a mixed boundary value problem of place and traction that describes the straightening of annular cylindrical sectors composed of unconstrained isotropic hyperelastic solids. The existence and uniqueness of solutions is discussed and several examples are exhibited. This revised version was published online in July 2006 with corrections to the Cover Date.     

Neumann Boundary-Value Problem for a Singularly Perturbed Heat Equation with Pulse Action

We propose an algorithm for the construction of an asymptotic solution of the Neumann boundary-value problem for a singularly perturbed heat equation with pulse action at fixed times. A theorem on the order with which the asymptotic solution satisfies the original problem is proved.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 89–122, January–March, 2005.     

On a Boundary-Value Problem of Periodic Type for First-Order Linear Functional Differential Equations

We establish unimprovable sufficient conditions for the unique solvability of the boundary-value problem

Domain of Convergence of an Iteration Procedure for a Weakly Nonlinear Boundary-Value Problem

We obtain estimates for the values of a small parameter for which the iteration procedure used for the construction of solutions of the Noetherian weakly nonlinear boundary-value problem for a system of ordinary differential equations is convergent in both critical and noncritical cases. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 278–288, April–June, 2005.     

Asymptotic Solution for a Kind of Boundary Layer Problem

This paper studies the partial differential equation with a small coefficient in the highest-order item. This kind of equation is also named as boundary layer problem. The Burgers equation and modified Burgers equation are analyzed in this approach. First, these equations are transferred into the strong nonlinear ones, and then the corresponding strong nonlinear equations are solved based on the perturbation method. The results from the asymptotic method are comparable with those obtained from numerical computation. An erratum to this article is available at .     

Contact Problem for a Narrow Annular Punch. Unknown Region of Contact

The nonlinear problem of determining the contact stresses and the contact zone under the base of a narrow annular punch is studied. An asymptotic model of one–sided contact along the line is constructed by the method of matched asymptotic expansions. Explicit asymptotic formulas for the line–pressure density are obtained. The asymptotic representation of the contact arc is given.     

Boundary-Value Problem of Drainage in a Fresh Groundwater Fringe above Saline Groundwater

A multiparameter boundary-value problem of fresh infiltration water seepage in a drained fringe above quiescent saline water is solved in the direct statement and studied in detail.     

Dynamic Contact Problem for a Plane with a Finite Crack

We study the contact interaction of the faces of a finite rectilinear crack under harmonic compression–expansion and shear waves incident at an arbitrary angle. An iterative algorithm based on the variational principles of elastic theory is used. The contact interaction and displacement discontinuity of the crack faces are analyzed. The crack-tip stress intensity factors are calculated. The results are compared with those obtained regardless of the contact interaction     

Analysis of Tracked-Vehicle Suspension Systems Using a Frictional Contact Problem Formulation

ABSTRACT

A new procedure for analysis of tracked-vehicle suspension systems under a track length constraint, based on a frictional contact problem formulation, is presented. Impenetrability, inextensibility, unilateral behavior of track, and friction conditions are expressed in complementarity form. The resulting problem is then amenable to efficient numerical algorithms, such as the modified simplex method. This approach is demonstrated through numerical applications to a model of a tracked-vehicle suspension system.     

On a Boundary-Value Problem of Antiperiodic Type for First-Order Nonlinear Functional Differential Equations of Non-Volterra Type

We establish unimprovable (in a certain sense) sufficient conditions for the solvability and unique solvability of the boundary-value problem

Contact Problem for Porous Elastic Half-Plane

The paper is concerned with a static contact problem about a rigid punch on the free surface of a linear porous elastic half-plane. With the use of the Fourier transform the problem is reduced to a singular integral equation holding over the contact zone. This integral representation permits consideration of the Flamant problem (a line load on the half-plane) to be explicitly reduced to some quadratures. It is shown that in the classical linear elasticity limit the main integral equation has a Cauchy-type kernel, so distribution of the contact pressure is like in the Sadowsky punch-problem. For arbitrary porosity a numerical co-location technique is applied that allows one to analyze in detail the distribution of the contact pressure versus porosity. Both in the Flamant and Sadowsky problems we demonstrate a higher compliance of the porous foundation, with respect to the classical linear elastic results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asymptotic Methods Applied to Contact Problems

Asymptotic methods for contact problems are expounded. Some typical integral equations are considered     

Solution of the Stochastic Boundary-Value Problem of Steady-State Creep for a Thick-Walled Tube Using the Small-Parameter Method

The physically and statistically nonlinear problem of steady-state creep for a thick-walled tube loaded by internal pressure is solved in the third approximation using the small-parameter method. The variances of random creep strain rates and displacements are calculated. The results obtained are compared with the solution of the same problem in the first and second approximations. A reliability assessment method for the tube using the strain failure criteria is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 161–171, January–February, 2006.     

Analysis of the Singularity for the Vertical Contact Problem of Line Crack-Inclusion

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Contact Problem for an Elastic Orthotropic Half-Strip

The paper discusses the problem on a rigid flat-based die forced into a half-strip. The material of the half-strip, whose semiinfinite sides are fixed, is orthotropic; the principal axes of anisotropy coincide with the Cartesian coordinate axes. Friction between the die and the half-strip is taken into account. The problem is solved by an asymptotic method developed by the authors. Some numerical results are presented     

Homogenization of a Boundary-Value Problem with Varying type of Boundary Conditions in a Thick Two-Level Junction

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω _ɛ that is the union of a domain Ω₀ and a large number 2N of thin rods with thickness of order ɛ = (N ⁻¹). Depending on their lengths, the thin rods are divided into two levels. In addition, the rods from each level are ɛ-periodically alternated. Inhomogeneous Neumann boundary conditions are given on the vertical sides of the thin rods of the first level, and homogeneous Dirichlet boundary conditions are given on the vertical sides of the rods of the second level. We investigate the asymptotic behavior of a solution of this problem as ɛ → 0 and prove a convergence theorem and the convergence of the energy integral. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 241–257, April–June, 2005.     

Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space

The paper is concerned with a contact problem about rigid rectangular punch forced into a half-space made of a linear elastic isotropic material with voids. We use a Cowin–Nunziato model for the half-space, and reduce the problem to a double Fredholm integral equation of the first kind. Then we apply two different approaches, to solve this equation. The first one is based on a direct collocation numerical technique. The second method is asymptotic, and we use a small parameter that is the relative width of the punch. Finally, compliance of the punch is determined, and results of the two different methods are compared with each other, as well as with a Sivashinsky–Panek–Kalker solution. Mathematics Subject Classifications (2000) 74M15.