Modélisation H ============== Caractéristiques de la modélisation ----------------------------------- Élément de coque triangulaire COQUE_3D. Le modèle de plaque associé à la modélisation :math:`E` est tourné de 20 degrés suivant l’angle nautique alpha et de 30 degrés suivant bêta. La numérotation des mailles est identique à celle de la modélisation :math:`E` . .. image:: images/10000000000001AB000001C95D135D313E860762.png :width: 4.3591in :height: 4.6638in .. _RefImage_10000000000001AB000001C95D135D313E860762.png: Conditions aux limites: .. csv-table:: "LIAISON_OBLIQUE" "(GROUP_NO: AB, ANGL_NAUT=(20.,30.,0.),DX: 0.,DZ: 0.,DRY:0.)" "(GROUP_NO: BC, ANGL_NAUT=(20.,30.,0.),DY: 0.,DZ: 0.,DRX:0.)" "(GROUP_NO: CD, ANGL_NAUT=(20.,30.,0.),DX: 0.,DZ: 0.,DRY:0.)" "(GROUP_NO: DA, ANGL_NAUT=(20.,30.,0.),DY: 0.,DZ: 0.,DRX:0.)" "(GROUP_NO: O , ANGL_NAUT=(20.,30.,0.),DX: 0.,DY: 0.,DRX:0.,DRY:0.,DRZ:0.)" "FORCE_ARETE" "(GROUP_NO: AB MY:0.)" "(GROUP_NO: BC MX:0.)" "(GROUP_NO: CD MY:0.)" "(GROUP_NO: DA MX:0.)" Caractéristiques du maillage ---------------------------- Nombre de nœuds : 626 Nombre de mailles et type : 288 TRIA6 Grandeurs testées et résultats ------------------------------ +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | **Identification** | +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`O` | :math:`(\mathit{M134})`| Contraintes :math:`{\sigma}_{xx}` , :math:`{\sigma}_{yy}` , :math:`{\sigma}_{xy}` , :math:`{\sigma}_{xz}` , :math:`{\sigma}_{yz}` sur feuillets inférieur, milieu et supérieur | | | | | | | | Déplacement :math:`\mathit{DZ}` | +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{B1}`| :math:`(\mathit{M122})`| Contraintes :math:`{\sigma}_{xx}` , :math:`{\sigma}_{yy}` , :math:`{\sigma}_{xy}` , :math:`{\sigma}_{xz}` , :math:`{\sigma}_{yz}` sur feuillets inférieur, milieu et supérieur | +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | **Identification** | +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`O` | :math:`(\mathit{M134})`| :math:`N_{xx}` , :math:`N_{yy}` , :math:`N_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` et :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | + +------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | :math:`(\mathit{M158})`| :math:`T_{x}` , :math:`T_{y}` | + +------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | :math:`(\mathit{M132})`| :math:`T_{x}` , :math:`T_{y}` | + +------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | :math:`(\mathit{M156})`| :math:`T_{x}` , :math:`T_{y}` | +--------------------------+------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+ +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | **Identification** | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{A}` | :math:`(\mathit{M1})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{B}` | :math:`(\mathit{M266})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{C}` | :math:`(\mathit{M288})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{D}` | :math:`(\mathit{M23})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | **Identification** | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{B1}`| :math:`(\mathit{M122})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | + +-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | :math:`(\mathit{M146})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | **Identification** | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Point :math:`\mathit{D1}`| :math:`(\mathit{M11})` | :math:`{T}_{x}` , :math:`{T}_{y}` | + +-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | :math:`(\mathit{M14})` | :math:`{N}_{xx}` , :math:`{N}_{yy}` , :math:`{N}_{xy}` , :math:`{M}_{xx}` , :math:`{M}_{yy}` , :math:`{M}_{xy}` , :math:`{T}_{x}` , :math:`{T}_{y}` | +--------------------------+-------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Remarques --------- La valeur de référence du déplacement au point :math:`O` est obtenue en projetant le déplacement calculé pour la modélisation E dans le repère tourné (le déplacement pour la modélisation E étant vertical, le nouveau déplacement est fonction de la projection de l’axe :math:`Z` ). Dans le repère local, la projection de l’axe :math:`Z` est la suivante: .. math:: \begin{pmatrix} \sin \beta \cos \alpha \\ \sin \beta \sin \alpha \\ \cos \beta \end{pmatrix}, \text{ avec } \alpha = 20. \text{ et } \beta = 30. D’autre part, l’expression de la pression sinusoïdale dans le repère tourné devient: .. math:: P = f_0 \sin \pi \frac{\cos \alpha \cos \beta x + \sin \alpha \cos \beta y - \sin \beta z}{a} \sin \pi \frac{\cos \alpha y - \sin \alpha x}{a}