G modeling ============== Characteristics of modeling ----------------------------------- Modeling of a quarter cylinder. Plate elements DKT: TRIA3. The modeling uses a bi-layer plate whose orthotropy characteristics are those of the material defined in :math:`\S 1.2`. .. image:: images/Object_17.svg :width: 288 :height: 192 .. _RefImage_Object_17.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 types: 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}`. G modeling results ------------------------------ +-----------------------+-----------------------------------+---------------------+-------------+ |**Identification** |**Knot (mesh)** |**Value tested** |**Reference**| +-----------------------+-----------------------------------+---------------------+-------------+ |**Gravity** |:math:`K` |:math:`\mathrm{DX}` |—2.40000 10—8| + +-----------------------------------+---------------------+-------------+ | |:math:`N` |:math:`\mathrm{DY}` |—2.40000 10—8| + +-----------------------------------+---------------------+-------------+ | |:math:`P` |:math:`\mathrm{DZ}` |5.0 10—9 | + +-----------------------------------+---------------------+-------------+ | |:math:`Q` |:math:`\mathrm{DZ}` |5.0 10—9 | + +-----------------------------------+---------------------+-------------+ | |:math:`P` |:math:`-\mathrm{DRY}`|2.40000 10—9 | + +-----------------------------------+---------------------+-------------+ | |:math:`Q` |:math:`\mathrm{DRX}` |2.40000 10—9 | + +-----------------------------------+---------------------+-------------+ | |:math:`K(\mathrm{M362})` |:math:`\mathrm{NYY}` |8.00000 10—4 | + +-----------------------------------+---------------------+-------------+ | |:math:`N(\mathrm{M400})` |:math:`\mathrm{NYY}` |8.00000 10—4 | + +-----------------------------------+---------------------+-------------+ | |:math:`K(\mathrm{M362})` |:math:`\mathrm{SIYY}`|8.00000 10—4 | + +-----------------------------------+---------------------+-------------+ | |:math:`N(\mathrm{M400})` |:math:`\mathrm{SIYY}`|8.00000 10—4 | +-----------------------+-----------------------------------+---------------------+-------------+ | | | | | +-----------------------+-----------------------------------+---------------------+-------------+ |**Dilation** **case 1**|:math:`L(\mathrm{M1})` |:math:`\mathrm{MYY}` |—2.38095 10—1| + +-----------------------------------+---------------------+-------------+ | |:math:`M(\mathrm{M39})` |:math:`\mathrm{MYY}` |—2.38095 10—1| + +-----------------------------------+---------------------+-------------+ | |:math:`L(\mathrm{M1})`, inner skin |:math:`\mathrm{SIXX}`|1.428571 | + +-----------------------------------+---------------------+-------------+ | |:math:`L(\mathrm{M1})`, outer skin |:math:`\mathrm{SIXX}`|— 1.428571 | + +-----------------------------------+---------------------+-------------+ | |:math:`M(\mathrm{M39})`, inner skin|:math:`\mathrm{SIXX}`|1.428571 | + +-----------------------------------+---------------------+-------------+ | |:math:`M(\mathrm{M39})`, outer skin|:math:`\mathrm{SIXX}`|— 1.428571 | +-----------------------+-----------------------------------+---------------------+-------------+ | | | | | +-----------------------+-----------------------------------+---------------------+-------------+ |**Dilation** **case 2**|:math:`L` |:math:`\mathrm{DX}` |26.0 10—6 | + +-----------------------------------+---------------------+-------------+ | |:math:`M` |:math:`\mathrm{DY}` |26.0 10—6 | + +-----------------------------------+---------------------+-------------+ | |:math:`L(\mathrm{M1})` |:math:`\mathrm{NYY}` |—2.00000 10—1| + +-----------------------------------+---------------------+-------------+ | |:math:`M(\mathrm{M39})` |:math:`\mathrm{NYY}` |—2.00000 10—1| + +-----------------------------------+---------------------+-------------+ | |:math:`L(\mathrm{M1})` |:math:`\mathrm{SIYY}`|—2.00000 10—1| + +-----------------------------------+---------------------+-------------+ | |:math:`M(\mathrm{M39})` |:math:`\mathrm{SIYY}`|—2.00000 10—1| +-----------------------+-----------------------------------+---------------------+-------------+