D modeling ============== Characteristics of modeling ----------------------------------- We use a AXIS model. Two calculations are carried out with different pairing options. In this model, the imposed crush goes up to :math:`10\mathit{mm}`. Characteristics of the mesh ---------------------------- .. image:: images/100000000000036A00000321DD90D58B2C6C9B6F.png :width: 4.822in :height: 4.4465in .. _RefImage_100000000000036A00000321DD90D58B2C6C9B6F.png: Knots: 243. Stitches: 100 TRIA3, 162 QUAD4. Tested sizes and results ------------------------------ .. _DdeLink__25432_345370281: First calculation (method 'PENALISATION', smoothing) +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ |**Identification** |**Reference type**|**Reference value**|**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |7.0% | + .. image:: images/Object_48.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |1.0% | + .. image:: images/Object_142.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |15.0% | + .. image:: images/Object_51.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |5.0% | + .. image:: images/Object_55.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |3.0% | + .. image:: images/Object_59.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |15.0% | + .. image:: images/Object_63.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |2.0% | + .. image:: images/Object_150.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |3.0% | + .. image:: images/Object_156.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |14.0% | + .. image:: images/Object_162.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |3.0% | + .. image:: images/Object_166.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |4.0% | + .. image:: images/Object_170.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`M286` knot :math:`N55(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |15.0% | + .. image:: images/Object_174.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`M293` knot :math:`N55(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |6.0% | + .. image:: images/Object_178.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`M31` knot :math:`N291(G)` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |4.0% | + .. image:: images/Object_182.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`M286` knot :math:`N55(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |15.0% | + .. image:: images/Object_186.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`M293` knot :math:`N55(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ Second calculation (method 'CONTRAINTE', nodal and normal slave pairing) +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ |**Identification** |**Reference type**|**Reference value**|**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |2.0% | + .. image:: images/Object_198.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |1.0% | + .. image:: images/Object_203.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |4.0% | + .. image:: images/Object_208.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_213.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_218.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |4.0% | + .. image:: images/Object_223.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |18.0% | + .. image:: images/Object_228.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |13.0% | + .. image:: images/Object_233.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |3.0% | + .. image:: images/Object_238.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |28.0% | + .. image:: images/Object_243.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |20.0% | + .. image:: images/Object_248.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |2.0% | + .. image:: images/Object_253.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |38.0% | + .. image:: images/Object_258.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |27.0% | + .. image:: images/Object_263.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |1.0% | + .. image:: images/Object_268.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ Third calculation (method 'CONTINUE', smoothing) +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ |**Identification** |**Reference type**|**Reference value**|**Tolerance**| +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |7.5% | + .. image:: images/Object_10.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`1.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |1.0% | + .. image:: images/Object_99.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |15.0% | + .. image:: images/Object_123.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |5.0% | + .. image:: images/Object_879.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`2.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |3.0% | + .. image:: images/Object_884.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |15.0% | + .. image:: images/Object_889.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |2.0% | + .. image:: images/Object_894.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`3.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |3.0% | + .. image:: images/Object_899.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |14.0% | + .. image:: images/Object_904.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |4.0% | + .. image:: images/Object_909.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`4.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |4.0% | + .. image:: images/Object_914.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |15.0% | + .. image:: images/Object_919.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |9.0% | + .. image:: images/Object_924.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`5.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |4.0% | + .. image:: images/Object_929.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |15.0% | + .. image:: images/Object_934.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ notes --------- The mesh consists of 2 hemispheres meshed differently (the upper sphere is in QUAD4, the lower sphere in TRIA3). The contact pressure measured on the upper surface is in good agreement with the analytical solution (the difference of the order of 5% is explained by extrapolation). On the lower surface, on the contrary, there are significant differences because there are 2 cells that conspire at point :math:`G\text{'}` (mesh of TRIA3), however, if we average the results obtained on these 2 cells, we find a pressure in good agreement with the analytical solution. With regard to the second calculation, the significant errors are due to the use of a nodal pairing while the mesh is not compatible.