F modeling ============== Characteristics of modeling ----------------------------------- Modeling a quarter cylinder. Plate elements DKT: TRIA3 .. image:: images/Object_16.svg :width: 288 :height: 192 .. _RefImage_Object_16.svg: Discretized geometry is shown above. .. csv-table:: "point", "knot" ":math:`K` "," :math:`\mathrm{NO1}`" ":math:`L` "," :math:`\mathrm{NO11}`" ":math:`M` "," :math:`\mathrm{NO161}`" ":math:`N` "," :math:`\mathrm{NO227}`" ":math:`P` "," :math:`\mathrm{NO6}`" ":math:`Q` "," :math:`\mathrm{NO215}`" Characteristics of the mesh ---------------------------- Number of knots: 231 Number of meshes and type: 400 TRIA3 + 80 SEG2 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}`. 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}`. F modeling results ------------------------------ +-----------------------+-----------------------------------+-----------------------------------+-------------+ |**Identification** |**Knot (mesh)** |**Value tested** |**Reference**| +-----------------------+-----------------------------------+-----------------------------------+-------------+ | | | | | +-----------------------+-----------------------------------+-----------------------------------+-------------+ |**Gravity** |:math:`K` |:math:`\mathrm{DX}(\mathrm{mm})` |—2.40000 10—8| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`N` |:math:`\mathrm{DY}(\mathrm{mm})` |—2.40000 10—8| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`P` |:math:`\mathrm{DZ}(\mathrm{mm})` |5.00000 10—9 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`Q` |:math:`\mathrm{DZ}(\mathrm{mm})` |5.00000 10—9 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`-\mathrm{DRX}` |:math:`-\mathrm{DRY}` |2.40000 10—9 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`\mathrm{DRX}` |:math:`\mathrm{DRX}` |2.40000 10—9 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`K(\mathrm{M362})` |:math:`\mathrm{NYY}(N)` |8.00000 10—4 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`N(\mathrm{M400})` |:math:`\mathrm{NYY}(N)` |8.00000 10—4 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`L(\mathrm{M362})` Inner skin|:math:`\mathrm{SIYY}(\mathrm{MPa})`|8.00000 10—4 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`N(\mathrm{M400})` Inner skin|:math:`\mathrm{SIYY}(\mathrm{MPa})`|8.00000 10—4 | +-----------------------+-----------------------------------+-----------------------------------+-------------+ | | | | | +-----------------------+-----------------------------------+-----------------------------------+-------------+ |**Dilation** **case 1**|:math:`L(\mathrm{M1})` |:math:`\mathrm{MYY}(\mathrm{N.mm})`|—2.38095 10—1| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`M(\mathrm{M39})` |:math:`\mathrm{MYY}(\mathrm{N.mm})`|—2.38095 10—1| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`L(\mathrm{M1})` Inner skin |:math:`\mathrm{SIXX}(\mathrm{MPa})`|1.428571 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`M(\mathrm{M39})` Inner skin |:math:`\mathrm{SIXX}(\mathrm{MPa})`|1.428571 | +-----------------------+-----------------------------------+-----------------------------------+-------------+ | | | | | +-----------------------+-----------------------------------+-----------------------------------+-------------+ |**Dilation** **case 2**|:math:`L` |:math:`\mathrm{DX}(\mathrm{mm})` |26.0000 10—6 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`M` |:math:`\mathrm{DY}(\mathrm{mm})` |26.0000 10—6 | + +-----------------------------------+-----------------------------------+-------------+ | |:math:`L(\mathrm{M1})` |:math:`\mathrm{NYY}(N)` |—2.00000 10—1| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`M(\mathrm{M39})` |:math:`\mathrm{NYY}(N)` |—2.00000 10—1| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`L(\mathrm{M1})` Inner skin |:math:`\mathrm{SIYY}(\mathrm{MPa})`|—2.00000 10—1| + +-----------------------------------+-----------------------------------+-------------+ | |:math:`M(\mathrm{M39})` Inner skin |:math:`\mathrm{SIYY}(\mathrm{MPa})`|—2.00000 10—1| +-----------------------+-----------------------------------+-----------------------------------+-------------+