D modeling ============== Characteristics of modeling ----------------------------------- Incompressible AXI elements (TRIA6 + QUAD8) .. image:: images/1000125A00002D7A00000E0E17035B052F36D7EF.svg :width: 586 :height: 181 .. _RefImage_1000125A00002D7A00000E0E17035B052F36D7EF.svg: For the purposes of stripping, the nodes are defined: * :math:`\mathrm{NOEUMIA}=A+(0.0.01/4)` where the deformations and stresses are the same as in :math:`A` * :math:`\mathrm{NOEUMIB}=B+(0.0.01/4)` where the deformations and stresses are the same as in :math:`B` Boundary conditions: .. code-block:: text DDL_IMPO = GROUP_NO =' FACSUP ', DY = 0 :math:`y=0.1` GROUP_NO =' FACINF ', DY = 0 :math:`y=0` PRES_REP = GROUP_MA =' FACEAE ', PRES = 60 sided :math:`\mathrm{AE}` Characteristics of the mesh ---------------------------- Number of knots: 175. Number of meshes and types: 20 QUAD8, 40 TRIA6. Tested sizes and results ------------------------------ Results at point :math:`A`: * first column AXIS_INCO_UPG without imposing :math:`\mathrm{GONF}=0` * second column AXIS_INCO_UPG by imposing :math:`\mathrm{GONF}=0` * third column AXIS_INCO_UP with quadratic mesh * fourth column AXIS_INCO_UP with linear mesh * fifth column AXIS_INCO_UPO with linear elements +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |**Identification** |**Reference type**|**Reference value**|**Tolerance** | + + + +-------------+-----+-----+-----+-----+ | | | |**1** |**2**|**3**|**4**|**5**| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`u` |'ANALYTIQUE' | #. 10 -5 |0.10% |0.10%|0.10%|0.10%|0.10%| + + + + + + + + + | | | | | | | | | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`v` |'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{xx}}` |'ANALYTIQUE' |—60. |0.50% |0.50%|0.50%|0.70%|1.50%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{yy}}` |'ANALYTIQUE' |03/20/12 |0.50% |0.50%|0.50%|1.00%|9.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{zz}}` |'ANALYTIQUE' | |0.50% |0.50%|0.50%|0.50%|6.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{xy}}` |'ANALYTIQUE' | |10-5 |0.01 |10-5 |0.08 |0.2 | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{xx}}` |'ANALYTIQUE' |-6. 10-4 |0.50% |0.50%|0.50%|0.60%|0.60%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{yy}}` |'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{xy}}` |'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{eq}}` - INVA_2|'ANALYTIQUE' |6.92 10-4 |0.50% |0.50%|0.50%|0.50%|3.0% | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_1|'ANALYTIQUE' |—6. 10-4 |0.50% |0.50%|0.50%|1.00%|6.0% | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_2|'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_3|'ANALYTIQUE' | #. 10-4 |0.50% |0.50%|0.50%|0.50%|0.60%| + + + + + + + + + | | | | | | | | | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - VMIS |'ANALYTIQUE' |138.56 |1.00% |1.00%|1.00%|1.00%|3.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - TRESCA |'ANALYTIQUE' | |1.00% |1.00%|1.00%|1.00%|3.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - PRIN_1 |'ANALYTIQUE' |-60. |1.00% |1.00%|1.00%|1.00%|2.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - PRIN_2 |'ANALYTIQUE' | |1.00% |1.00%|1.00%|1.00%|23.% | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - PRIN_3 |'ANALYTIQUE' | |1.00% |1.00%|1.00%|1.00%|5.5% | +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ |:math:`{\sigma }_{\mathrm{eq}}` - VMIS |'ANALYTIQUE' |138.56 |1.00% |1.00%|1.00%|1.00%|3.00%| +---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+ Results at point :math:`F`: * first column AXIS_INCO_UPG without imposing :math:`\mathrm{GONF}=0` * second column AXIS_INCO_UPG by imposing :math:`\mathrm{GONF}=0` * third column AXIS_INCO_UP with quadratic mesh * fourth column AXIS_INCO_UP with linear mesh * fifth column AXIS_INCO_UPO with linear elements +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |**Identification** |**Reference type**|**Reference value**|**Tolerance** | + + + +-------------+------------+-------------+-----+-----+ | | | |**1** |**2** |**3** |**4**|**5**| +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`u` |'ANALYTIQUE' | #. 10-5 |0.10% |0.10% |0.10% |0.10%|2.0% | + + + + + + + + + | | | | | | | | | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`v` |'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\sigma }_{\mathrm{xx}}` |'ANALYTIQUE' | |0.03 |0.03 |0.03 |0.10 |0.70 | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\sigma }_{\mathrm{yy}}` |'ANALYTIQUE' | |0.50% |0.50% |0.50% |0.50%|1.1% | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\sigma }_{\mathrm{zz}}` |'ANALYTIQUE' | |0.50% |0.50% |0.50% |0.50%|0.60%| +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\sigma }_{\mathrm{xy}}` |'ANALYTIQUE' | | #. 10-3 | #. 10- | #. 10-3 |0.01 |0.2 | + + + + + + + + + | | | | | | | | | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\varepsilon }_{\mathrm{xx}}`|'ANALYTIQUE' |-1.5 10-4 |0.50% |0.50% |0.50% |0.50%|1.0% | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\varepsilon }_{\mathrm{yy}}`|'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ |:math:`{\varepsilon }_{\mathrm{xy}}`|'ANALYTIQUE' | |10-5 |10-5 |10-5 |10-5 |10-5 | +------------------------------------+------------------+-------------------+-------------+------------+-------------+-----+-----+ Checking the transition to the nodes for the middle nodes (only for the result obtained without imposing :math:`\mathrm{GONF}=0`) :math:`\mathrm{NOEUMIA}` .. csv-table:: "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance (** :math:`\text{\%}` **)**" ":math:`{\sigma }_{\mathrm{xx}}` ", "'ANALYTIQUE'", "-60. "," 0.50%" ":math:`{\sigma }_{\mathrm{yy}}` ", "'ANALYTIQUE'", "20. "," 0.50%" ":math:`{\sigma }_{\mathrm{zz}}` ", "'ANALYTIQUE'", "100. "," 0.50%" ":math:`{\varepsilon }_{\mathrm{xx}}` ", "'ANALYTIQUE'", "-6. 10—4"," 0.50%" ":math:`{\varepsilon }_{\mathrm{yy}}` ", "'ANALYTIQUE'", "6. 10—4"," 0.50%" :math:`\mathrm{NOEUMIB}` .. csv-table:: "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance (** :math:`\text{\%}` **)**" ":math:`{\sigma }_{\mathrm{xx}}` ", "'ANALYTIQUE'", "0. "," 0.50%" ":math:`{\sigma }_{\mathrm{yy}}` ", "'ANALYTIQUE'", "20. "," 0.50%" ":math:`{\sigma }_{\mathrm{zz}}` ", "'ANALYTIQUE'", "40. "," 0.50%" ":math:`{\varepsilon }_{\mathrm{xx}}` ", "'ANALYTIQUE'", "-1.5 10—4"," 0.50%" ":math:`{\varepsilon }_{\mathrm{yy}}` ", "'ANALYTIQUE'", "1.5 10—4"," 0.50%" notes --------- The precision obtained is very good.