Viene applicata la teoria della Nota I al problema al contorno dell'elastostatica quando sul contorno vengono prescritte forze nulle. I coefficienti elastici sono supposti solo limitati e misurabili. Viene fatta un'analisi dettagliata per determinare l'operatore base.
Viene applicata la teoria della Nota I al problema al contorno dell'elastostatica quando sul contorno vengono prescritte condizioni miste. I coefficienti elastici sono supposti solo limitati e misurabili. Viene fatta un'analisi dettagliata per determinare l'operatore base. Si fa inoltre vedere come i problemi di trasmissione, relativi a due o più solidi elastici non isotropi e non omogenei incastrati l'uno nell'altro, rientrano nella teoria sviluppata nelle Note precedenti.
Viene applicata la teoria della Nota I al problema al contorno dell'elastostatica quando sul contorno vengono prescritti spostamenti nulli. I coefficienti elastici sono supposti solo limitati e misurabili. Come problema base viene assunto l'analogo problema al contorno per un corpo isotropo omogeneo. Per un tale problema vengono esplicitamente costruiti l'operatore e la matrice di Green e le loro proprietà esaurientemente studiate, in modo tale che la teoria degli operatori intermedi, come sviluppata...
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input state” map in -norms is established. A structure of the reachable sets for arbitrary is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input → state" map in L2-norms is established. A structure of the reachable sets for arbitrary T>0 is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section...
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.