Summary of results ====================== **% of differences compared to the reference solutions** +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |**DKT** | |**DKQ** |**DST** |**DSQ** |**Q4G** | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |A |B |E |F |G |H | + + + + + + + + | | Love-Kirchhoff | Love-Kirchhoff | Love-Kirchhoff | Reissner | Reissner | Reissner | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |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 |—1.10 |—0.09 |—0.09 |+0.12 |—0.11 |—0.15 | + + + + + + + + | | | | | | | | + .. image:: images/Object_130.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |D |—1.01 |—0.1 |—0.11 |+0.08 |—0.13 |—0.20 | + + + + + + + + | | | | | | | | + .. image:: images/Object_131.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |E |—1.03 |—0.09 |—0.12 |+0.09 |—0.13 |—0.20 | + + + + + + + + | | | | | | | | + .. image:: images/Object_132.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |F |—1.05 |—0.09 |—0.09 |+0.07 |—0.15 |—0.21 | + + + + + + + + | | | | | | | | + .. image:: images/Object_133.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |**MEC3QU9H** |**MEC3TR7H** | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |I |J | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | |96 knots |121 knots | | | | | + + + + + + + + | | 25 QUAD9 | 50 TRIA7 | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |O |1.42 10 —3 |—0.03 | | | | | + + + + + + + + | | | | | | | | + .. image:: images/Object_134.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |D | #. 10 —3 |—0.07 | | | | | + + + + + + + + | | | | | | | | + .. image:: images/Object_135.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |E | #. 10 —3 |—0.07 | | | | | + + + + + + + + | | | | | | | | + .. image:: images/Object_136.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ |F | | | | | | | + + + + + + + + | | | | | | | | + .. image:: images/Object_137.svg + + + + + + + | :width: 33 | | | | | | | + :height: 21 + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | + + + + + + + + | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ | | | | | | | | +---------------------------------------------------------------------------------------------------------+--------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+----------------------------------+ Regarding travel: Plate and shell elements give good results on fairly coarse meshes. .. csv-table:: "", "**DKT**", "", "**DKQ**", "****", "**DST**", "**DSQ**", "**Q4G**" "", "A Love-Kirchhoff", "B Love-Kirchhoff", "E Love-Kirchhoff", "F Reissner", "G Reissner", "H Reissner" "", "50 knots 76 TRIA3 ", "170 knots 296 TRIA3 ", "169 knots 147 QUAD4 ", "170 knots 296 TRIA3 ", "169 knots 147 QUAD4 ", "169 knots 147 QUAD4" "O Sm/2", "—1.19", "+0.02", "+0.02", "+0.07", "+0.07", "—0.76", "—0.14" "A Sm/2", "+5.79", "—0.06", "—0.06", "—0.49", "—4.40", "—9.80", "+17.80" "B Sm/2", "—13.100", "—5.100", "—5.53", "+1.00", "—9.10", "—7.12", "+19.70" "C Sm/2", "+5.73", "—0.06", "—0.06", "—0.46", "—4.41", "—9.44", "+17.90" "D Sm/2", "+0.20", "+0.35", "+0.35", "+0.50", "+0.43", "+0.49", "+0.05" "E Sm/2", "+0.19", "+0.19", "+0.42", "+0.50", "+0.50", "+0.50", "+0.05" "F Sm/2", "—0.66", "+0.25", "—0.25", "—0.30", "+0.15", "+19.00", "—0.33" "", "**MEC3QU9H**", "**MEC3TR7H**", "", "", "", "", "" "", "I", "J", "", "", "", "" "", "96 knots 25 QUAD9 ", "121 knots 50 TRIA7 ", "", "", "", "" "O Sm/2", "1.05", "1.14", "", "", "", "", "" "A Sm/2", "2.9", "0.25", "", "", "", "", "" "B Sm/2", "-", "-", "-", "", "", "", "" "C Sm/2", "2.9", "0.25", "", "", "", "", "" "D Sm/2", "0.28", "—0.28", "", "", "", "", "" "E Sm/2", "0.28", "—0.28", "", "", "", "", "", "" "F Sm/2", "-", "-", "-", "", "", "", "" Regarding the efforts: * On the pressed edge, significant errors (up to 20%) are observed compared to analytical solutions. The error is the most pronounced on modeling :math:`H` (Q4G). * by refining the mesh of each model, we observe the convergence of efforts, that is to say that the error tends towards 0. However, the order of convergence is lower for modeling :math:`H`: the Q4G element requires in fact to mesh very finely in the directions stressed during bending (it uses a bilinear approximation of the rotations whereas modeling DST is based on a quadratic approximation).