B modeling ============== Characteristics of modeling ------------------------ Axisymmetric shell elements .. image:: images/1000045000000EC8000018CE03D68347C69B2FAD.svg :width: 162 :height: 272 .. _RefImage_1000045000000EC8000018CE03D68347C69B2FAD.svg: Discretized geometry is shown above. The Love‑Kirchhoff shell theory is chosen (for this purpose a transverse shear coefficient of 106 is taken). The metric correction in thickness is neglected. The thickness is :math:`1\mathrm{mm}`. .. csv-table:: "knot", "GROUP_NO" ":math:`J` "," :math:`\mathrm{GRNO13}`" ":math:`H` "," :math:`\mathrm{GRNO14}`" ":math:`F` "," :math:`\mathrm{GRNO6}`" Characteristics of the mesh ---------------------------- Number of knots: 21 Number of meshes and type: 10 SEG3 Boundary conditions in movement and rotation --------------------------------- Gravity ~~~~~~~~ Move :math:`\mathrm{DY}` is stuck at point :math:`F` alone (:math:`\mathrm{GRNO6}`). Rotation ~~~~~~~ Move :math:`\mathrm{DY}` is stuck at point :math:`F` (:math:`\mathrm{GRNO6}`) at point :math:`J` (:math:`\mathrm{GRNO13}`). The rotation around the :math:`Z` axis is zero at these two points. Thermal expansion case no. 1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The movement :math:`\mathrm{DY}` as well as the rotation around the axis :math:`Z` are blocked throughout the structure (GROUP_NO = 'GRNO15'). Thermal expansion case no. 2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Move :math:`\mathrm{DY}` is stuck at point :math:`F` (GROUP_NO = 'GRNO06') and at point :math:`J` (GROUP_NO = 'GRNO13'). The rotation around the :math:`Z` axis is zero on the same node groups. B modeling results ------------------------------ +--------------------------------+----------------------------------+-----------------------------------+-------------+ |**Identification** |**Knot (Knit)** |**Value tested** |**Reference**| +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ |**Gravity** |:math:`J` |:math:`\mathrm{DX}(\mathrm{mm})` |—2.40000 10—8| + +----------------------------------+-----------------------------------+-------------+ | |:math:`H` |:math:`\mathrm{DY}(\mathrm{mm})` |5.00000 10—9 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`H` |:math:`\mathrm{DRZ}` |2.40000 10—9 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`J(\mathrm{M10})` |:math:`\mathrm{NXX}(N)` |8.00000 10—4 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`J(\mathrm{M10})` Inner skin|:math:`\mathrm{SIXX}(\mathrm{MPa})`|8.00000 10—4 | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ |**Rotation - centrifugal force**|:math:`F` |:math:`\mathrm{DX}(\mathrm{mm})` |2.91200 10—7 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`F(\mathrm{M1})` |:math:`\mathrm{NXX}(N)` |9.60000 10—4 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`F(\mathrm{M1})` Inner skin |:math:`\mathrm{SIXX}(\mathrm{MPa})`|9.60000 10—4 | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ |**Dilation** **case 1** |:math:`F(\mathrm{M1})` |:math:`\mathrm{MXX}(\mathrm{N.mm})`|—2.38095 10—1| + +----------------------------------+-----------------------------------+-------------+ | |:math:`F(\mathrm{M1})` Inner skin |:math:`\mathrm{SIXX}(\mathrm{Mpa})`|1.428571 | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+ |**Dilation** **case 2** |:math:`F` |:math:`\mathrm{DX}(\mathrm{mm})` |26.0000 10—6 | + +----------------------------------+-----------------------------------+-------------+ | |:math:`F(\mathrm{M1})` |:math:`\mathrm{NXX}(N)` |—2.00000 10—1| + +----------------------------------+-----------------------------------+-------------+ | |:math:`F(\mathrm{M1})` Inner skin |:math:`\mathrm{SIXX}(\mathrm{MPa})`|—2.00000 10—1| +--------------------------------+----------------------------------+-----------------------------------+-------------+ | | | | | +--------------------------------+----------------------------------+-----------------------------------+-------------+