Uniform resolvent convergence for strip with fast oscillating boundary

In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change.     

A fully-analytical approach for modelling the response of FRP plates bonded to a brittle substrate

Composite materials, such as fiber reinforced polymers (FRP), are more and more common as strengthening solution for existing structures. Adhesion between FRP and the existing substrate generally represents one of the main concerns on the effectiveness of these techniques. The bond behaviour of composite materials on concrete substrates (but also steel, masonry and wooden ones) are generally investigated by means of pull-out tests. The present paper, starting from the most common assumptions of the mechanical behaviour of the various materials, proposes a fully-analytical formulation for determining the response in terms of the relationship between the external force and the corresponding maximum interface slip observed in those tests. The proposed approach emphasises the key behavioural differences between “short” and “long” bonding length. The former are characterised by a softening behaviour of the relationship between the applied force and the maximum slip, while the latter exhibits a numerically challenging snap-back behaviour. All the key points of the relationship between the external force and the maximum interface slip are defined in closed-form for both the above mentioned cases. Finally, a comparison with some experimental results obtained on FRP-to-concrete pull-out tests are proposed.     

Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary

In this paper the asymptotic behaviour of a second-order linear evolution problem is studied in a domain, a part of wich has an oscillating boundary. An homogeneous Neumann condition is given on the whole boundary of the domain. Moreover the behaviour of associated optimal control problem is analyzed.      

Quasy-stationary ferromagnetic thin films in degenerated cases

In this paper we study the asymptotic behavior of a quasy-stationary ferromagnetic problem in a multi-domain consisting of two joined thin films. It is possible to distinguish different regimes depending on the limit \(q\) of the ratio between the small thickness of the two films. Here the case \(q=0\) and \(q=+\infty \) are analyzed.     

Junction problem for elastic and rigid inclusions in elastic bodies

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.