Keyword COQUE ==== Affordable characteristics ---- The characteristics that can be affected on the plate or shell elements are: • for all elements of this type, a constant thickness on each mesh, since the mesh represents only the middle sheet (or sketch for the eccentric ones), • for all elements of this type, the number of layers used for integration into the thickness, • for all elements of this type, the orientation of the local coordinate system specific to each mesh, • for some shell models, particular characteristics: shear coefficient, metric, eccentricity, etc. Syntax ---- COQUE = _F ( ♦ GROUP_MA = lgma, [l_gr_mesh] ♦/EPAIS = ep, [real] /EPAIS_FO = epfct [function] ◊/ANGL_REP =/(0.0, 0.0), [default] /(:math:`\alpha`, :math:`\beta`), [l_real] /VECTEUR = (vx, vy, vz), [l_real] ◊ MODI_METRIC = ['NO'|'YES'], [default)] ◊ COEF_RIGI_DRZ = KRZ (1.E-5), [real (default)] ◊ EXCENTREMENT = e (0.0), [real (default)] EXCENTREMENT_FO = effect [function] ◊ INER_ROTA = 'OUI', ◊ A_CIS = kappa (0.8333333), [real (default)] ◊ COQUE_NCOU = n (1), [integer (default)] )))) Operands ---- Operand EPAIS ~~~~ ♦/EPAIS = ep /EPAIS_FO = perfect EPAIS represents the thickness of the shell, which should be expressed in the same units as the coordinates of the mesh nodes. EPAIS_FO is a function that gives the thickness of the shell, in the same units as the coordinates of the mesh nodes. This function depends on the geometry (X, Y, Z) and is evaluated at the center of gravity of the mesh. Operands EXCENTREMENT/EXCENTREMENT_FO ~~~~ ◊ eccentricity =/e (0.0), [real (default)] eccentrement_F0 = effect [function] eccentricity: define the distance between the mesh surface and the mean surface, in the normal direction (models DKT, DST, GRILLE_EXCENTRE). Excentrement_fo: Function that gives the distance between the mesh surface and the average surface, in the normal direction (models DKT, DST, GRILLE_EXCENTRE). This function depends on the geometry (X, Y, Z) and is evaluated at the center of gravity of the mesh. Taking into account the eccentricity affects the flexural behavior and possibly on the membrane behavior in the presence of coupling (there is no effect on shear). Operands MODI_METRIQUE/COEF_RIGI_DRZ/INER_ROTA ~~~~ ◊ modi_metric = 'no' Assumes that the thickness of the element is small. When integrating into the thickness, the variation in the radius of curvature is not taken into account (option by default for all shells). ◊ modi_metric = 'yes' For modeling: COQUE_AXIS, the integrations are made taking into account the variations in the radius of curvature as a function of the thickness, see for example [:ref:`R3.07.02 `] ◊ iner_rota = 'yes' Taking rotational inertia into account for modeling DKT, DST and Q4G. It is mandatory in case of eccentricity. This keyword can be omitted for thin shells, where the rotational inertia terms are negligible compared to the others in the mass matrix [:ref:`R3.07.03 `]. ◊ coef_rigi_drz = krz, KRZ is a fictional stiffness coefficient (necessarily small) on the degree of freedom of rotation around the normal to the shell. It is necessary to prevent the stiffness matrix from being singular, but should be chosen as small as possible. The default value of :math:`{10}^{-5}` is suitable for most situations (it's a relative value: the stiffness around the normal is KRZ times the smallest diagonal term in the element's stiffness matrix). For DKT, there are two modes of operation. COEF_RIGI_DRZ negative and COEF_RIGI_DRZ positive. In the positive COEF_RIGI_DRZ case, the degree of freedom DRZ always has a fictional direction of rotation that prevents the matrix from being singular in the global coordinate system. In the case of a negative COEF_RIGI_DRZ, the kinematics of rotation of the plate element around its normal is reinforced by variational writing. So the DRZ degree of freedom makes physical sense. We recommend a value of :math:`{10}^{-8}`. **Note:** *Attention, in* *STAT/DYNA_NON_LINE, this coefficient can lead to additional Newton iterations (more than one iteration for a linear problem for example) .* Operand ANGL_REP/VECTEUR ~~~~ The keywords ANGL_REP or VECTEUR make it possible to fill in the "user" coordinate system in each shell element. It is in this frame of reference that, for example, constraints in the shell or generalized efforts are expressed [:ref:`U2.01.05 `]. Using these keywords, the user provides a :math:`V` vector that will allow the coordinate system to be fully defined. The construction of this "user" coordinate system from :math:`V` is carried out at all points :math:`P` in the following way (cf. figure): • the projection of :math:`V` on the tangential plane provides the :math:`{x}_{l}` axis, • the vector :math:`{z}_{l}` is collinear to the normal :math:`n` at the plane of the shell which is known for each element, its orientation can be changed by MODI_MAILLAGE/ORIE_NORM_COQUE [U4.23.04], • the vector :math:`{y}_{l}` is constructed in such a way as to have an orthonormal coordinate system. The "user" frame of reference is therefore: :math:`(P,{x}_{l},{y}_{l},{z}_{l})` with: :math:`{z}_{l}=n` and :math:`{y}_{l}={z}_{l}\text{^}{x}_{l}` .. image:: images/100000000000038E000001FB107DF684E73A04F7.png :width: 3.8646in :height: 2.0425in .. _RefImage_100000000000038E000001FB107DF684E73A04F7.png: Figure 8.3.4-1: Definition of the user coordinate system of a shell The ANGL_REPet VECTEURsont keywords are exclusive, the vector :math:`V` is defined using one or the other. ◊ ANGL_REP = (:math:`\alpha`, :math:`\beta`) The keyword ANGL_REP defines the vector :math:`V` in the global coordinate system :math:`(O,X,Y,Z)` from two nautical angles :math:`\alpha` and :math:`\beta` as explained Figure and Figure. +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | | + .. image:: images/10000000000000D4000000CC6447164A2E752507.png + .. image:: images/10000000000000E0000000C912CE860EFDE01A82.png + | :width: 2.878in | :width: 3.0665in | + :height: 2.7563in + :height: 2.7563in + | | | + **Figure** 8.3.4-2 **: Representation of the angle** :math:`\alpha` Rotation :math:`\alpha` around :math:`\mathrm{OZ}` turns :math:`(\mathrm{OXYZ})` into :math:`({\mathrm{OX}}_{1}{Y}_{1}Z)` with :math:`{Z}_{1}\equiv Z`. + **Figure** 8.3.4-3 **: Representation of the angle** :math:`\beta` Rotation :math:`\beta` around :math:`{\mathrm{OY}}_{1}` turns :math:`{\mathrm{OX}}_{1}` into :math:`{\mathrm{OX}}_{2}`. Note: in the figure, angle :math:`\beta` is negative. + | | | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ In three-dimensional representation, the vector is obtained as follows [Figure]. .. image:: images/100000000000015A0000014335D2F26124046702.png :width: 3.378in :height: 3.1492in .. _RefImage_100000000000015A0000014335D2F26124046702.png: **Figure** 8.3.4-4 **: 3D representation of the vector** :math:`V` **defined by** ANGL_REP ◊ VECTEUR = :math:`(\mathrm{vx},\mathrm{vy},\mathrm{vz})` Vector :math:`V` is defined by its coordinates in the global coordinate system :math:`(O,X,Y,Z)`. **Notes:** *•* *If none of the above keywords are entered, it is therefore the global axis* :math:`X` *that determines, by projection onto the tangential plane of the shell, the "user" coordinate system for each mesh.* *•* *The "user" coordinate system is also used to define the orientation of fibers in composite shells (DEFI_COMPOSITE,* [:external:ref:`U4.42.03 `] *) .* Operand COQUE_NCOU ~~~~ ◊ COQUE_NCOU =/n (1), [integer, default] This is the number of layers used to integrate into the thickness of the shell. The number of layers also determines the number of subpoints in the constraint field: :math:`2n+1`. In non-linear, it is necessary to use more than one layer to correctly integrate the constraints into the thickness, *cf.* [:ref:`U2.02.01 `]. Operand A_CIS ~~~~ ◊ A_CIS =/kappa (0.8333333), [real, default] This parameter is to be used if it is desired, for a thick shell, to be located within the framework of the Love-Kirchhoff model. It is only applicable for models COQUE_C_PLAN, COQUE_D_PLAN,, COQUE_AXIS, and COQUE_3D. For more details the user should refer to the manual [:ref:`U2.02.01 `]. Note on using ELAS_COQUE ~~~~ When using ELAS_COQUE the flexural and membrane stiffness are entered manually by the user in DEFI_MATERIAU. In this case, the thickness entered in AFFE_CARA_ELEM is only used to calculate the mass dynamically and does not contribute to the stiffness. .. _RefHeading__31234306: