This paper concerns an equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin rigid inclusion. It is assumed that the inclusions have a joint point and we analyze a junction problem for these inclusions. The existence of solutions is proved and the different equivalent formulations of the problem are discussed. In particular, the junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, the inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. We investigate the convergence to infinity and zero of a rigidity parameter of the elastic inclusion. It is proved that in the limit, we obtain a rigid inclusion and a zero rigidity inclusion (a crack).

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We study the contact problems for elastic plates with a rigid inclusion. We consider the case of frictionless contact between the rigid part of the plate and a rigid obstacle. The contact is modeled with the Signorini-type nonpenetration condition. The deformation of the transversely isotropic elastic part of the plate is described by the Timoshenko model. We analyze the dependence of solutions to the contact problems on the size of rigid inclusion. The existence of a solution to the optimal control problem is proved. For that problem, the cost functional characterizes the deviation of the displacement vector from a given function, whereas the size parameter of rigid inclusion is chosen as the control function.MSC: Primary 74G55; 49J40; secondary 49J30

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We studied the effect of drugs with various mechanisms of action on propulsive activity of the small intestine in healthy rats. Blockade of the major inhibitory influences realized via nonadrenergic noncholinergic inhibitory effector neurons was not followed by stimulation of intestinal transit. Propulsive activity of the small intestine increased upon treatment with drugs, whose effects are realized via acetylcholine or acetylcholine and serotonin.

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.

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.

We consider a plane visco-elastic body, composed of Maxwell material, with a crack and a thin rigid inclusion. The statement of the problem includes boundary conditions in the form of inequalities, together with an integral condition describing the equilibrium conditions of the inclusion. An equivalent variational statement is provided and used to prove the uniqueness of the problem's solution. The analysis is carried out in respect of perfect and non-perfect bonding of the rigid inclusion. Additional smoothness properties of the solutions, namely the existence of the time derivative, are also established.