Unilateral contact problem for two plates with a rigid inclusion in the lower plate

Попова

2017

Z Angew Math Mech

In the paper, an equilibrium problem for elastic bodies with a thin elastic Timoshenko inclusion and a thin semirigid inclusion is analyzed. The inclusions are assumed to be delaminated from elastic bodies, thus forming a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. The inclusions have a joint point. A passage to a limit is investigated as a rigidity parameter of the elastic inclusion goes to infinity. The limit model is investigated. Junction boundary conditions are found at the joint point for the problem analyzed as well as for the limit problem.

“…At this point, we can mention other approaches to describe inclusions in elastic bodies . As for junction problems for elastic structures we refer the reader to publications , see also .…”

Section: Introductionmentioning

confidence: 99%

On the mechanical interplay between Timoshenko and semirigid inclusions embedded in elastic bodies

Попова

2017

Z Angew Math Mech

“…Optimal control problems for such models can be found in [15,[33][34][35]. Volume rigid inclusions in elastic bodies are analyzed in [9,26,28]; see also [37].…”

Section: Introductionmentioning

confidence: 99%

Junction problem for rigid and semirigid inclusions in elastic bodies

Попова

2016

Arch Appl Mech

The paper is concerned with equilibrium problems for 2D elastic bodies having thin inclusions with different properties. In particular, rigid and semirigid inclusions are considered. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved for each equilibrium problem, and different equivalent formulations of these problems are discussed. In particular, junction conditions at the joint point are found. A delamination of the inclusions is also assumed. This means that we have a crack, and inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We discuss a convergence to zero and infinity of a rigidity parameter of the semirigid inclusion and analyze limit problems.

“…Finding the derivatives of the energy functionals is important from the standpoint of the Griffith rupture criterion [11][12][13][14][15]. Existence theorems and qualitative properties of solutions in equilibrium problems for elastic bodies with thin and volume rigid inclusions can be found in [5,[16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Junction problem for elastic and rigid inclusions in elastic bodies

Faella

Math Methods in App Sciences

2015

An equilibrium problem for an elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. We analyze a junction problem assuming that the inclusions have a joint point. Different equivalent problem formulations are discussed, and existence of solutions is proved. A set of junction conditions is found. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusion. A delamination of the elastic inclusion is also investigated. In this case, inequality‐type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. Copyright © 2015 John Wiley & Sons, Ltd.