F modeling ============== Characteristics of modeling ----------------------------------- We use a AXIS model. Four calculations are performed with different matching options or contact algorithms. Characteristics of the mesh ---------------------------- .. image:: images/100000000000036A00000321F96CDE73DCFEB23F.png :width: 4.822in :height: 4.4465in .. _RefImage_100000000000036A00000321F96CDE73DCFEB23F.png: Knots: 376 knots. Meshes: 30 TRIA3 and 324 QUAD4. Tested sizes and results ------------------------------ First calculation (nodal pairing, master-slave normal and algorithm 'PENALISATION') +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |**Identification** |**Reference type**|**Reference value** |**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_345.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)` |'ANALYTIQUE' |0 :math:`\mathit{mm}` |1.0E-10 | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,110211 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,162912 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0,165946 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0.629667 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ Second calculation (normal master-slave, algorithm 'PENALISATION') +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |**Identification** |**Reference type**|**Reference value** |**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_368.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)` |'ANALYTIQUE' |0 :math:`\mathit{mm}` |1.0E-10 | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,110678 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,162865 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0,167194 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0.628961 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ Third calculation (normal master-slave, algorithm 'CONTRAINTE') +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |**Identification** |**Reference type**|**Reference value** |**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_391.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)` |'ANALYTIQUE' |0 :math:`\mathit{mm}` |1.0E-10 | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,110678 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,162901 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0,167194 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0.628947 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ Fourth calculation (smoothing, master-slave normal and algorithm 'CONTRAINTE') +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |**Identification** |**Reference type**|**Reference value** |**Tolerance**| +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ | |'ANALYTIQUE' |-2798.3 :math:`N` |7.0% | + .. image:: images/Object_414.svg + + + + | :width: 26 | | | | + :height: 24 + + + + | | | | | + mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)` + + + + | | | | | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)` |'ANALYTIQUE' |0 :math:`\mathit{mm}` |1.0E-10 | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,110211 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)` |'NON_REGRESSION' |-0,162911 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0,165946 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ |:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)` |'NON_REGRESSION' |-0.629666 :math:`\mathit{mm}`| | +-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+ notes --------- On this modeling, we note that smoothing makes it possible to regain the symmetry of the problem (nodes perfectly facing each other once contact has been established), the last calculation in fact obtaining the same results as in nodal matching. The values obtained are in good general agreement with the analytical solutions.