G modeling ============== Characteristics of modeling ----------------------------------- We use a AXIS model. Two calculations are performed 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 ------------------------------ First calculation (smoothing, master-slave normal and algorithm 'PENALISATION') +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ |**Identification** |**Reference type**|**Reference value**|**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |8.0% | + .. image:: images/Object_438.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_443.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_448.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |6.0% | + .. image:: images/Object_453.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |4.0% | + .. image:: images/Object_458.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_463.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |1.0% | + .. image:: images/Object_468.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_473.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_478.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |4.0% | + .. image:: images/Object_483.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |3.0% | + .. image:: images/Object_488.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |14.5% | + .. image:: images/Object_493.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |8.0% | + .. image:: images/Object_498.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |3.0% | + .. image:: images/Object_503.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |15.0% | + .. image:: images/Object_508.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ Second calculation (smoothing, master-slave normal and algorithm 'CONTRAINTE') +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ |**Identification** |**Reference type**|**Reference value**|**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-1978.7 :math:`N` |8.0% | + .. image:: images/Object_513.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_518.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_523.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`1.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |6.0% | + .. image:: images/Object_528.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |4.0% | + .. image:: images/Object_533.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_538.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`2.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3427.2 :math:`N` |1.0% | + .. image:: images/Object_543.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_548.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_553.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`3.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |4.0% | + .. image:: images/Object_558.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |3.0% | + .. image:: images/Object_563.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-3957.4 :math:`N` |14.0% | + .. image:: images/Object_568.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M293}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`4.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |8.0% | + .. image:: images/Object_573.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |3.0% | + .. image:: images/Object_578.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :math:`\mathit{M286}` knot :math:`\mathit{N55}(G\text{'})` instant :math:`5.0` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------+-------------------+-------------+ | |'ANALYTIQUE' |-4424.5 :math:`N` |15.0% | + .. image:: images/Object_583.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + stitch :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. The two contact algorithms used give substantially the same results. .. _ddelink__4833_2082477356: