Summary of results ====================== **% of differences compared to the reference solutions** +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |**DKT** | |**DKQ** |**DST** |**DSQ** |**Q4G** | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |Fashionable. |A |B |E |F |G |H | + + + + + + + + | | Love- | Kirchhoff | Love-Kirchhoff | Reissner | Reissner | Reissner | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |Point |50 knots |170 knots |169 knots |170 knots |169 knots |169 knots | + + + + + + + + | | 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 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |D |—0.23 |+0.18 |+0.23 |+0.77 |+0.19 |—0.28 | + + + + + + + + | | | | | | | | + .. image:: images/Object_148.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |E |—0.25 |+0.24 |+0.23 |+0.84 |+0.19 |—0.28 | + + + + + + + + | | | | | | | | + .. image:: images/Object_149.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |F |—0.32 |+0.22 |+0.20 |+0.75 |+0.14 |—0.34 | + + + + + + + + | | | | | | | | + .. image:: images/Object_150.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ +---------------------------------------------------------------------------------------------------------+-------------------------+ | |**Q4G** | +---------------------------------------------------------------------------------------------------------+-------------------------+ |Fashionable. |M | + + + | | Reissner | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |Point |561 knots - 1036 TRIA3 | +---------------------------------------------------------------------------------------------------------+-------------------------+ |O |+0.176 | + + + | | | + .. image:: images/Object_58.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |D |+0.225 | + + + | | | + .. image:: images/Object_280.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |E |+0.225 | + + + | | | + .. image:: images/Object_281.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |F | | + + + | | | + .. image:: images/Object_282.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ | |**COQU_AXIS** |**MEC3QU9H** |**MEC3TR7H** | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |Fashionable. |I Love-Kirchhoff|J Reissner|K |L | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |Point |21 knots 10 SEG3| |96 knots 25 QUAD9|121 knots 50 TRIA7| +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |O |+0.51 |0.03 |—0.16 |—0.13 | + .. image:: images/Object_151.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |D |+0.28 |0.05 |—0.029 |—0.35 | + .. image:: images/Object_152.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |E | | |—0.029 |—0.35 | + .. image:: images/Object_153.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |F | |+0.22 | | | + .. image:: images/Object_154.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |**DKT** | |**DKQ** |**DST** |**DSQ** |**Q4G** | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |Fashionable. |A |B |E |F |G |H | + + + + + + + + | | Love- | Kirchhoff | Love-Kirchhoff | Reissner | Reissner | Reissner | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |Point |50 knots |170 knots |169 knots |170 knots |169 knots |169 knots | + + + + + + + + | | 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 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |A |+0.81 |+4.02 |+0.49 |+5.26 |+3.79 |—10.73 | + + + + + + + + | | | | | | | | + .. image:: images/Object_156.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |B |+4.58 |+2.64 |+0.20 |+2.02 |+1.69 |—10.95 | + + + + + + + + | | | | | | | | + .. image:: images/Object_157.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |C |+0.75 |+4.13 |+0.45 |+5.34 |+3.64 |—10.69 | + + + + + + + + | | | | | | | | + .. image:: images/Object_158.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |D |+4.55 |+1.99 |+2.71 |+2.07 |+0.40 |+0.74 | + + + + + + + + | | | | | | | | + .. image:: images/Object_159.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |E |+4.55 |+2.19 |+2.71 |+2.29 |+0.40 |+0.74 | + + + + + + + + | | | | | | | | + .. image:: images/Object_160.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |F |+1.71 |+2.05 |—0.79 |+1.19 |+17.80 |—0.94 | + + + + + + + + | | | | | | | | + .. image:: images/Object_161.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ +---------------------------------------------------------------------------------------------------------+-------------------------+ | |**Q4G** | +---------------------------------------------------------------------------------------------------------+-------------------------+ |Fashionable. |M | + + + | | Reissner | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |Point |561 knots - 1036 TRIA3 | +---------------------------------------------------------------------------------------------------------+-------------------------+ |O |+0.265 | + + + | | | + .. image:: images/Object_283.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |A |+1.65 | + + + | | | + .. image:: images/Object_284.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |B |+4.95 | + + + | | | + .. image:: images/Object_285.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |C |+1.73 | + + + | | | + .. image:: images/Object_286.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |D |+5.18 | + + + | | | + .. image:: images/Object_287.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |E |+5.50 | + + + | | | + .. image:: images/Object_288.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ |F |+4.07 | + + + | | | + .. image:: images/Object_289.svg + + | :width: 33 | | + :height: 21 + + | | | + + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------+-------------------------+ +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ | |**COQU_AXIS** |**MEC3QU9H** |**MEC3TR7H** | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |Fashionable. |I Love-Kirchhoff|J Reissner|K |L | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |Point |21 knots 10 SEG3| |96 knots 25 QUAD9|121 knots 50 TRIA7| +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |O |+0.18 |+0.62 |2.67 |2.89 | + .. image:: images/Object_162.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |A |+14.2 |—1.01 |—1.45 |—1.33 | + .. image:: images/Object_163.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |B | | | | | + .. image:: images/Object_164.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |C | | |—1.46 |—1.32 | + .. image:: images/Object_165.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |D |+0.84 |—0.85 |1.08 |—1.23 | + .. image:: images/Object_166.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |E | | |0.95 |—1.23 | + .. image:: images/Object_167.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ |F | | | | | + .. image:: images/Object_168.svg + + + + + | :width: 33 | | | | | + :height: 21 + + + + + | | | | | | + + + + + + | | | | | | +-------------------------------------------------------------------------------------+----------------+----------+-----------------+------------------+ **Note** s **:** *Regarding efforts, direct calculation at the nodes leads to discrepancies in several nodes, especially at point F in* *DSQet on the edge* :math:`\mathrm{ABC}` *en* *Q4G.* Modeling with COQUE_SOLIDE elements (N modeling) is the only plate modeling that accounts for the pinch effect with a linear constraint in the thickness.