Search

In the paper, we consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion crossing an external boundary. The elastic body has a defect which is characterized by a positive damage parameter. The presence of a defect means that the problem is formulated in a non-smooth domain. Non-linear boundary conditions at the defect faces are imposed to prevent the mutual penetration between the faces. Both variational and differential problem formulations are proposed, and existence of solutions is established. We study an asymptotics of solutions with respect to the damage parameter as well as with respect to a rigidity parameter of the inclusion. Identification problems for finding the damage parameter are investigated. To this end, existence of solutions of optimal control problems is proven. [ABSTRACT FROM AUTHOR]

In the paper, we consider an equilibrium problem for a 2D elastic body with thin Euler-Bernoulli and Timoshenko elastic inclusions. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved, and different equivalent formulations of the problem are discussed. In particular, junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusions. Limit problems are analyzed. [ABSTRACT FROM AUTHOR]

We consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion. It is assumed that the inclusion is partially delaminated, therefore providing the presence of a crack. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration of the faces. Differentiability properties of the energy functional with respect to the crack length are analyzed. We prove an existence of the derivative and find a formula for this derivative. It is shown that the formula for the derivative can be written in the form of a singular invariant integral. [ABSTRACT FROM AUTHOR]