| Structures hétérogènes |  |
| Structures hétérogènes | |
| HAL : hal-00691024, version 1 |
| DOI : 10.1016/j.euromechsol.2009.05.006 |
| Fiche détaillée |  Récupérer au format |
 |
| EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 28, 6 (2009) 1051-1063 |
|
|
|
|
| Bounds for the effective properties of heterogeneous plates |
|
|
| T. K. Nguyen 1K. Sab 1 |
|
|
| (06/05/2009) |
|
|
|
| This paper presents new bounds for heterogeneous plates which are similar to the well-known Hashin-Shtrikman bounds, but take into account plate boundary conditions. The Hashin-Shtrikman variational principle is used with a self-adjoint Green-operator with traction-free boundary conditions proposed by the authors. This variational formulation enables to derive lower and upper bounds for the effective in-plane and out-of-plane elastic properties of the plate. Two applications of the general theory are considered: first, in-plane invariant polarization fields are used to recover the "first-order" bounds proposed by Kolpakov [Kolpakov, A.G.,1999. Variational principles for stiffnesses of a non-homogeneous plate. J. Meth. Phys. Solids 47,2075-2092] for general heterogeneous plates; next, "second-order bounds" for n-phase plates whose constituents are statistically homogeneous in the in-plane directions are obtained The results related to a two-phase material made of elastic isotropic materials are shown. The "second-order" bounds for the plate elastic properties are compared with the plate properties of homogeneous plates made of materials having an elasticity tensor computed from "second-order" Hashin-Shtrikman bounds in an infinite domain. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire Navier |
|
|
|
Ecole des Ponts ParisTech – CNRS : UMR8205 – IFSTTAR |
|
|
| 2 : | Laboratoire de Modélisation et Simulation Multi Echelle (MSME) |
|
|
|
Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8208 |
|
|
|
|
|
|
|
|
|
| Matériaux et Structures Architecturés (MSA) |
|
|
|
|
| Domaine | : | Sciences de l'ingénieur/Mécanique/Mécanique des solides Physique/Mécanique/Mécanique des solides |
|
|
| NONLOCAL CONSTITUTIVE-EQUATIONS – GRADED COMPOSITE-MATERIALS – VOLUME ELEMENT SIZE – VARIATIONAL-PRINCIPLES – MICROMECHANICAL MODELS – MULTILAYERED PLATES – ELASTIC BEHAVIOUR – NUMERICAL-METHOD – LIMIT ANALYSIS – RANDOM-MEDIA |
|
| hal-00691024, version 1 | |
| http://hal-upec-upem.archives-ouvertes.fr/hal-00691024 | |
| oai:hal-upec-upem.archives-ouvertes.fr:hal-00691024 | |
| Contributeur : Guy Bonnet | |
| Soumis le : Mercredi 25 Avril 2012, 10:45:04 | |
| Dernière modification le : Mardi 2 Avril 2013, 12:26:43 | |
