Synthèse des résultats ====================== **% des différences par rapport aux solutions de référence** +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ | | **DKT** | | **DKQ** | **DST** | **DSQ** | **Q4G** | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |Modé. |A |B |E |F |G |H | | | Love- | Kirchhoff | Love-Kirchhoff | Reissner | Reissner | Reissner | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |Point |50 nœuds |170 nœuds |169 nœuds |170 nœuds |169 nœuds |169 nœuds | | | 76 TRIA3 | 296 TRIA3 | 147 QUAD4 | 296 TRIA3 | 147 QUAD4 | 147 QUAD4 | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |O |–0.76 |+0.12 |+0.22 |+0.74 |+0.19 |–0.08 | | | | | | | | | | .. image:: images/Object_147.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_147.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |D |–0.23 |+0.18 |+0.23 |+0.77 |+0.19 |–0.28 | | | | | | | | | | .. image:: images/Object_148.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_148.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |E |–0.25 |+0.24 |+0.23 |+0.84 |+0.19 |–0.28 | | | | | | | | | | .. image:: images/Object_149.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_149.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |F |–0.32 |+0.22 |+0.20 |+0.75 |+0.14 |–0.34 | | | | | | | | | | .. image:: images/Object_150.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_150.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ +----------------------------------+------------------------+ | | **Q4G** | +----------------------------------+------------------------+ |Modé. |M | | | Reissner | +----------------------------------+------------------------+ | Point | 561 nœuds - 1036 TRIA3 | +----------------------------------+------------------------+ |O |+0.176 | | | | | .. image:: images/Object_58.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_58.svg: | | | | | | | | +----------------------------------+------------------------+ |D |+0.225 | | | | | .. image:: images/Object_280.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_280.svg: | | | | | | | | +----------------------------------+------------------------+ |E |+0.225 | | | | | .. image:: images/Object_281.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_281.svg: | | | | | | | | +----------------------------------+------------------------+ |F |- | | | | | .. image:: images/Object_282.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_282.svg: | | | | | | | | +----------------------------------+------------------------+ +----------------------------------+---------------------------+--------------+--------------+ | | **COQU_AXIS** | **MEC3QU9H** | **MEC3TR7H** | +----------------------------------+----------------+----------+--------------+--------------+ | Modé. | I | J | K | L | | | Love-Kirchhoff | Reissner | | | +----------------------------------+----------------+----------+--------------+--------------+ | Point | 21 nœuds | | 96 nœuds | 121 nœuds | | | 10 SEG3 | | 25 QUAD9 | 50 TRIA7 | +----------------------------------+----------------+----------+--------------+--------------+ | O | +0.51 | 0.03 | –0.16 | –0.13 | | | | | | | | .. image:: images/Object_151.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_151.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | D | +0.28 | 0.05 | –0.029 | –0.35 | | | | | | | | .. image:: images/Object_152.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_152.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | E | - | - | –0.029 | –0.35 | | | | | | | | .. image:: images/Object_153.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_153.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | F | - | +0.22 | - | - | | | | | | | | .. image:: images/Object_154.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_154.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ | | **DKT** | | **DKQ** | **DST** | **DSQ** | **Q4G** | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |Modé. |A |B |E |F |G |H | | | Love- | Kirchhoff | Love-Kirchhoff | Reissner | Reissner | Reissner | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |Point |50 nœuds |170 nœuds |169 nœuds |170 nœuds |169 nœuds |169 nœuds | | | 76 TRIA3 | 296 TRIA3 | 147 QUAD4 | 296 TRIA3 | 147 QUAD4 | 147 QUAD4 | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |O |–1.15 |+0.19 |+0.46 |+1.04 |–0.33 |–0.07 | | | | | | | | | | .. image:: images/Object_155.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_155.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |A |+0.81 |+4.02 |+0.49 |+5.26 |+3.79 |–10.73 | | | | | | | | | | .. image:: images/Object_156.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_156.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |B |+4.58 |+2.64 |+0.20 |+2.02 |+1.69 |–10.95 | | | | | | | | | | .. image:: images/Object_157.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_157.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |C |+0.75 |+4.13 |+0.45 |+5.34 |+3.64 |–10.69 | | | | | | | | | | .. image:: images/Object_158.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_158.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |D |+4.55 |+1.99 |+2.71 |+2.07 |+0.40 |+0.74 | | | | | | | | | | .. image:: images/Object_159.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_159.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |E |+4.55 |+2.19 |+2.71 |+2.29 |+0.40 |+0.74 | | | | | | | | | | .. image:: images/Object_160.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_160.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ |F |+1.71 |+2.05 |–0.79 |+1.19 |+17.80 |–0.94 | | | | | | | | | | .. image:: images/Object_161.svg | | | | | | | | :width: 33 | | | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | | | | | | | .. _RefImage_Object_161.svg: | | | | | | | | | | | | | | | | | | | | | | | +----------------------------------+----------+-----------+----------------+-----------+-----------+-----------+ +----------------------------------+------------------------+ | | **Q4G** | +----------------------------------+------------------------+ |Modé. |M | | | Reissner | +----------------------------------+------------------------+ | Point | 561 nœuds - 1036 TRIA3 | +----------------------------------+------------------------+ |O |+0.265 | | | | | .. image:: images/Object_283.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_283.svg: | | | | | | | | +----------------------------------+------------------------+ |A |+1.65 | | | | | .. image:: images/Object_284.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_284.svg: | | | | | | | | +----------------------------------+------------------------+ |B |+4.95 | | | | | .. image:: images/Object_285.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_285.svg: | | | | | | | | +----------------------------------+------------------------+ |C |+1.73 | | | | | .. image:: images/Object_286.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_286.svg: | | | | | | | | +----------------------------------+------------------------+ |D |+5.18 | | | | | .. image:: images/Object_287.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_287.svg: | | | | | | | | +----------------------------------+------------------------+ |E |+5.50 | | | | | .. image:: images/Object_288.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_288.svg: | | | | | | | | +----------------------------------+------------------------+ |F |+4.07 | | | | | .. image:: images/Object_289.svg | | | :width: 33 | | | :height: 21 | | | | | | | | | .. _RefImage_Object_289.svg: | | | | | | | | +----------------------------------+------------------------+ +----------------------------------+---------------------------+--------------+--------------+ | | **COQU_AXIS** | **MEC3QU9H** | **MEC3TR7H** | +----------------------------------+----------------+----------+--------------+--------------+ | Modé. | I | J | K | L | | | Love-Kirchhoff | Reissner | | | +----------------------------------+----------------+----------+--------------+--------------+ | Point | 21 nœuds | | 96 nœuds | 121 nœuds | | | 10 SEG3 | | 25 QUAD9 | 50 TRIA7 | +----------------------------------+----------------+----------+--------------+--------------+ | O | +0.18 | +0.62 | 2.67 | 2.89 | | | | | | | | .. image:: images/Object_162.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_162.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | A | +14.2 | –1.01 | –1.45 | –1.33 | | | | | | | | .. image:: images/Object_163.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_163.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | B | - | - | - | - | | | | | | | | .. image:: images/Object_164.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_164.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | C | - | - | –1.46 | –1.32 | | | | | | | | .. image:: images/Object_165.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_165.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | D | +0.84 | –0.85 | 1.08 | –1.23 | | | | | | | | .. image:: images/Object_166.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_166.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | E | - | - | 0.95 | –1.23 | | | | | | | | .. image:: images/Object_167.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_167.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ | F | - | - | - | - | | | | | | | | .. image:: images/Object_168.svg | | | | | | :width: 33 | | | | | | :height: 21 | | | | | | | | | | | | | | | | | | .. _RefImage_Object_168.svg: | | | | | | | | | | | | | | | | | +----------------------------------+----------------+----------+--------------+--------------+ **Remarque** s **:** *Concernant les efforts, le calcul direct aux nœuds conduit à des écarts en plusieurs nœuds, notamment au point F en* *DSQet sur le bord* :math:`\mathrm{ABC}` *en* *Q4G.* La modélisation avec des éléments de type COQUE_SOLIDE (modélisation N) est la seule modélisation de plaque qui rend compte de l’effet de pincement avec une contrainte linéaire dans l’épaisseur.