C modeling ============== Characteristics of modeling ----------------------------------- Modeling of a quarter cylinder. 3D shell elements: QUAD9 .. image:: images/Object_13.svg :width: 288 :height: 192 .. _RefImage_Object_13.svg: Discretized geometry is shown above. .. csv-table:: ":math:`\mathrm{point}` "," :math:`\mathrm{nœud}`" ":math:`K` "," :math:`\mathrm{NO72}`" ":math:`L` "," :math:`\mathrm{NO1}`" ":math:`M` "," :math:`\mathrm{NO33}`" ":math:`N` "," :math:`\mathrm{NO39}`" ":math:`P` "," :math:`\mathrm{NO186}`" ":math:`Q` "," :math:`\mathrm{NO190}`" The shear correction factor :math:`{A}_{\mathrm{CIS}}` is :math:`5/6` (Reissner shell theory). Characteristics of the mesh ---------------------------- Number of external nodes: 121 Number of meshes and types: 32 QUAD9 + 8 SEG3 Boundary conditions in movement and rotation ------------------------------------------------- Gravity ~~~~~~~~ Move :math:`\mathrm{DZ}` is stuck on the group of nodes :math:`\mathrm{LM}`. The movement :math:`\mathrm{DY}` as well as the rotations around the axes :math:`X` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{KL}`. The movement :math:`\mathrm{DX}` as well as the rotations around the axes :math:`Y` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{MN}`. Rotation ~~~~~~~ The :math:`\mathrm{DZ}` movement as well as the rotations around the :math:`X` and :math:`Y` axes are blocked on the node groups :math:`\mathrm{KNSANSKN}` and :math:`\mathrm{LMSANSLM}`. The movement :math:`\mathrm{DY}` as well as the rotations around the axes :math:`X` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{KL}`. The movement :math:`\mathrm{DX}` as well as the rotations around the axes :math:`Y` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{MN}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`Y` axis are blocked on the group of nodes :math:`\mathrm{KETL}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`X` axis are blocked on the group of nodes :math:`\mathrm{METN}`. Thermal expansion case no. 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The :math:`\mathrm{DZ}` movement as well as the rotations around the :math:`X` and :math:`Y` axes are blocked on the node groups :math:`\mathrm{KNSANSKN}` and :math:`\mathrm{LMSANSLM}`. The movement :math:`\mathrm{DY}` as well as the rotations around the axes :math:`X` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{KL}`. The movement :math:`\mathrm{DX}` as well as the rotations around the axes :math:`Y` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{MN}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`Y` axis are blocked on the group of nodes :math:`\mathrm{KETL}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`X` axis are blocked on the group of nodes :math:`\mathrm{METN}`. Thermal expansion case no. 2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The :math:`\mathrm{DZ}` movement as well as the rotations around the :math:`X` and :math:`Y` axes are blocked on the node groups :math:`\mathrm{KNSANSKN}` and :math:`\mathrm{LMSANSLM}`. The movement :math:`\mathrm{DY}` as well as the rotations around the axes :math:`X` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{KL}`. The movement :math:`\mathrm{DX}` as well as the rotations around the axes :math:`Y` and :math:`Z` are blocked on the group of nodes :math:`\mathrm{MN}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`Y` axis are blocked on the group of nodes :math:`\mathrm{KETL}`. The :math:`\mathrm{DZ}` movement and the rotation around the :math:`X` axis are blocked on the group of nodes :math:`\mathrm{METN}`. C modeling results ------------------------------ +----------------------------+----------------------------------+--------------------------------------------+-------------+ |**Identification** |**Knot (mesh)** |**Value tested** |**Reference**| +----------------------------+----------------------------------+--------------------------------------------+-------------+ | | | | | +----------------------------+----------------------------------+--------------------------------------------+-------------+ |Gravity |:math:`K` |:math:`\mathrm{DX}` :math:`(\mathrm{mm})` |—2.40000 10—8| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`N` |:math:`\mathrm{DY}` :math:`(\mathrm{mm})` |—2.40000 10—8| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`P` |:math:`\mathrm{DZ}` :math:`(\mathrm{mm})` |5.00000 10—9 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`Q` |:math:`\mathrm{DZ}` :math:`(\mathrm{mm})` |5.00000 10—9 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`P` |:math:`\mathrm{DRY}` |2.40000 10—9 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`Q` |:math:`\mathrm{DRX}` |2.40000 10—9 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`K(\mathrm{M4})` |:math:`\mathrm{NYY}` :math:`(N)` |8.00000 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`N(\mathrm{M32})` |:math:`\mathrm{NYY}` :math:`(N)` |8.00000 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`K(\mathrm{M4})` Inner skin |:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|8.00000 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`N(\mathrm{M32})` Inner skin|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|8.00000 10—4 | +----------------------------+----------------------------------+--------------------------------------------+-------------+ | | | | | +----------------------------+----------------------------------+--------------------------------------------+-------------+ |Rotation — centrifugal force|:math:`L` |:math:`\mathrm{DX}` :math:`(\mathrm{mm})` |2.91200 10—7 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M` |:math:`\mathrm{DY}` :math:`(\mathrm{mm})` |2.91200 10—7 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`L(\mathrm{M1})` |:math:`\mathrm{NYY}` :math:`(N)` |9.60000 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` |:math:`\mathrm{NYY}` :math:`(N)` |9.60000 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`L(\mathrm{M1})` Inner skin |:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|9.84600 10—4 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` Inner skin|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|9.84600 10—4 | +----------------------------+----------------------------------+--------------------------------------------+-------------+ | | | | | +----------------------------+----------------------------------+--------------------------------------------+-------------+ |Dilation case 1 |:math:`L(\mathrm{M1})` |:math:`\mathrm{MYY}` :math:`(\mathrm{N.mm})`|—2.38095 10—1| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` |:math:`\mathrm{MYY}` :math:`(\mathrm{N.mm})`|—2.38095 10—1| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`L(\mathrm{M1})` Inner skin |:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|1.428571 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` Inner skin|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|1.428571 | +----------------------------+----------------------------------+--------------------------------------------+-------------+ | | | | | +----------------------------+----------------------------------+--------------------------------------------+-------------+ |Dilation case 2 |:math:`L` |:math:`\mathrm{DX}` :math:`(\mathrm{mm})` |25.9946 10—6 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M` |:math:`\mathrm{DY}` :math:`(\mathrm{mm})` |25.9946 10—6 | + +----------------------------------+--------------------------------------------+-------------+ | |:math:`L(\mathrm{M1})` |:math:`\mathrm{NYY}` :math:`(N)` |—2.00000 10—1| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` |:math:`\mathrm{NYY}` :math:`(N)` |—2.00000 10—1| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`L(\mathrm{M1})` Inner skin |:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|—1.97800 10—1| + +----------------------------------+--------------------------------------------+-------------+ | |:math:`M(\mathrm{M29})` Inner skin|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|—2.97800 10—1| +----------------------------+----------------------------------+--------------------------------------------+-------------+ notes --------- Satisfactory and identical results for calculations with MECA_STATIQUE and STAT_NON_LINE.