Multigrid methods for parameter dependent problems
Multiscale deformation analysis by Cauchy-Navier wavelets.
Multiscale expansion and numerical approximation for surface defects⋆
This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...
Multiscale finite element coarse spaces for the application to linear elasticity
We extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [Hou T.Y., Wu X.-H., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 1997, 134(1), 169–189] to the PDE system of linear elasticity. The application, motivated by the multiscale analysis of highly heterogeneous composite materials, is twofold. Resolving the heterogeneities on the finest scale, we utilize the linear MsFEM basis for the construction...
Napjatost a deformace homogenního poloprostoru transversálně isotropního při rovnoměrném zatížení povrchu v obdélníkově ploše
Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity
Neumann problem for one-dimensional nonlinear thermoelasticity
The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.
Non-classical phase transitions at a sonic point.
Nonlinear flexural excitations and drill-string dynamics.
Non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material
A direct proof of the non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material is given by means of a simple counter-example.
Nonstationary initial-boundary value contact problems of generalized elastothermodiffusion.
Non-stationary problems of generalized elastothermodiffusion for inhomogeneous media.
Note on a mixed variational principle in finite elasticity
In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.
Note sur les équations générales de la théorie mathématique de l'élasticité en coordonnées curvilignes
Nouvelles propriétés des courbes et relation de dispersion en élasticité linéaire
In the case of an elastic strip we exhibit two properties of dispersion curves λn,n ≥ 1, that were not pointed out previously. We show cases where λ'n(0) = λ''n(0) = λ'''n(0) = 0 and we point out that these curves are not automatically monotoneous on . The non monotonicity was an open question (see [2], for example) and, for the first time, we give a rigourous answer. Recall the characteristic property of the dispersion curves: {λn(p);n ≥ 1} is the set of eigenvalues of Ap, counted with their...
Nouvelles propriétés des courbes et relations de dispersion en élasticité linéaire
Numerical approximation of stiff transmission problems by mixed finite element methods
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type
A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...
On a boundary value problem in nonlinear theory of thin elastic plates
On a familiy of torsional creep problems.