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We introduce the space of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for , which leads to a compactness result for the space of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational...
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...
The 2D-Signorini contact problem with Tresca and Coulomb friction
is discussed in infinite-dimensional Hilbert spaces. First, the
problem with given friction (Tresca friction) is considered. It
leads to a constraint non-differentiable minimization problem. By
means of the Fenchel duality theorem this problem can be transformed
into a constrained minimization involving a smooth functional. A
regularization technique for the dual problem motivated by augmented
Lagrangians allows to apply an...
Bhattacharya and Kohn have used small-strain (geometrically linear)
elasticity to analyze the recoverable strains of shape-memory polycrystals.
The adequacy of small-strain theory is open to question, however, since some
shape-memory materials recover as much as 10 percent strain. This paper
provides the first progress toward an analogous geometrically nonlinear
theory. We consider a model problem, involving polycrystals made
from a two-variant elastic material in two space dimensions. The linear
theory...
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of the free boundary values variational problem. Such is, for instance, the problem of finding the shortest curve whose endpoints can slide along two prescribed curves. There exists a rigorous geometric way to formulate this sort of problems on smooth manifolds with boundary, which we review here in a friendly self-contained way. As an application,...
In this paper, a finite dimensional approximated model of a mechanical system constituted by a vertical heavy flexible beam with lumped masses placed along the beam and a mobile mass located at the tip, is proposed; such a model is parametric in the approximation order, so that a prescribed accuracy in the representation of the actual system can be easily obtained with the proposed model. The system itself can be understood as a simple representation of a building subject to transverse vibrations,...
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