308 research outputs found
Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency
The classical energy minimization principles of Dirichlet and Thompson are
extended as minimization principles to acoustics, elastodynamics and
electromagnetism in lossy inhomogeneous bodies at fixed frequency. This is done
by building upon ideas of Cherkaev and Gibiansky, who derived minimization
variational principles for quasistatics. In the absence of free current the
primary electromagnetic minimization variational principles have a minimum
which is the time-averaged electrical power dissipated in the body. The
variational principles provide constraints on the boundary values of the fields
when the moduli are known. Conversely, when the boundary values of the fields
have been measured, then they provide information about the values of the
moduli within the body. This should have application to electromagnetic
tomography. We also derive saddle point variational principles which correspond
to variational principles of Gurtin, Willis, and Borcea.Comment: 32 pages 0 figures (Previous version omitted references
Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation
The aim of this paper is to propose for the first time a reconstruction
scheme and a stability result for recovering from acoustic-optic data
absorption distributions with bounded variation. The paper extends earlier
results on smooth absorption distributions. It opens a door for a mathematical
and numerical framework for imaging, from internal data, parameter
distributions with high contrast in biological tissues
The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent. A review of existing results
In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces
On the forces that cable webs under tension can support and how to design cable webs to channel stresses
In many applications of Structural Engineering the following question arises:
given a set of forces applied at
prescribed points , under what
constraints on the forces does there exist a truss structure (or wire web) with
all elements under tension that supports these forces? Here we provide answer
to such a question for any configuration of the terminal points
in the two- and
three-dimensional case. Specifically, the existence of a web is guaranteed by a
necessary and sufficient condition on the loading which corresponds to a finite
dimensional linear programming problem. In two-dimensions we show that any such
web can be replaced by one in which there are at most elementary loops,
where elementary means the loop cannot be subdivided into subloops, and where
is the number of forces
applied at points strictly within the convex hull of
. In three-dimensions we show
that, by slightly perturbing ,
there exists a uniloadable web supporting this loading. Uniloadable means it
supports this loading and all positive multiples of it, but not any other
loading. Uniloadable webs provide a mechanism for distributing stress in
desired ways.Comment: 18 pages, 8 figure
Convergence of Hencky-type discrete beam model to euler inextensible elastica in large deformation: Rigorous proof
The present chapter concerns rigorous homogenization of a Hencky-type
discrete beam model, which is useful for the numerical study of complex fibrous
systems as pantographic sheets as well as woven fabrics. -convergence of the
discrete model towards the inextensible Euler’s beam model is proven and the result
is established for placements in Rd in large deformation regime
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