Simply-Supported 'Solid' Square Plate#
問題の説明#
10m×10m×1mのソリッド要素で構成された直方体のモーダル解析のベンチマークです。 The Standard NAFEMS BenchmarksにFV52として掲載されています。
条件#
ベンチマークに使用するメッシュは次の通りです。 HOEは2次要素、LOEは1次要素でメッシュのパターンが異なっています。
条件図を次に示します。 図の左端を並進拘束（XY拘束）し、全節点は奥行方向の並進拘束（Z拘束)しています。
入力する物性値は次の通りです。
材料物性 |
入力値 |
|---|---|
ヤング率 |
200E+9 N/m^2 |
ポアソン比 |
0.3 |
密度 |
8000 kg/m^3 |
結果と考察#
比較する結果は各モード次数での固有振動数の値です。 比較結果を示します。
Solver |
Pattern |
Type |
Order |
Shape |
Result |
Error |
|---|---|---|---|---|---|---|
Reference value |
1 |
45.897 |
‐ |
|||
Commercial code |
HOE |
C3D20 |
2 |
Hexa |
44.796 |
97.60% |
Commercial code |
LOE |
C3D8I |
1 |
Hexa |
44.092 |
96.07% |
Salome-Meca 2021 |
HOE |
3D |
2 |
Hexa |
44.796 |
97.60% |
Salome-Meca 2021 |
LOE |
3D |
1 |
Hexa |
51.679 |
112.60% |
Commercial code 2nd order elements (mode4)#
Commercial code 1st order elements (mode4)#
Salome-Meca 2019 2nd order elements (mode4)#
Salome-Meca 2019 1st order elements (mode4)#
Solver |
Pattern |
Type |
Order |
Shape |
Result |
Error |
|---|---|---|---|---|---|---|
Reference value |
1 |
109.44 |
‐ |
|||
Commercial code |
HOE |
C3D20 |
2 |
Hexa |
110.54 |
101.01% |
Commercial code |
LOE |
C3D8I |
1 |
Hexa |
106.66 |
97.46% |
Salome-Meca 2021 |
HOE |
3D |
2 |
Hexa |
110.54 |
101.01% |
Salome-Meca 2021 |
LOE |
3D |
1 |
Hexa |
132.75 |
121.30% |
Commercial code 2nd order elements (mode5&6)#
Commercial code 1st order elements (mode5&6)#
Salome-Meca 2019 2nd order elements (mode5&6)#
Salome-Meca 2019 1st order elements (mode5&6)#
Solver |
Pattern |
Type |
Order |
Shape |
Result |
Error |
|---|---|---|---|---|---|---|
Reference value |
1 |
167.89 |
‐ |
|||
Commercial code |
HOE |
C3D20 |
2 |
Hexa |
169.10 |
100.72% |
Commercial code |
LOE |
C3D8I |
1 |
Hexa |
156.23 |
93.05% |
Salome-Meca 2021 |
HOE |
3D |
2 |
Hexa |
169.10 |
100.72% |
Salome-Meca 2021 |
LOE |
3D |
1 |
Hexa |
194.38 |
115.78% |
Commercial code 2nd order elements (mode7)#
Commercial code 1st order elements (mode7)#
Salome-Meca 2019 2nd order elements (mode7)#
Salome-Meca 2019 1st order elements (mode7)#
Solver |
Pattern |
Type |
Order |
Shape |
Result |
Error |
|---|---|---|---|---|---|---|
Reference value |
1 |
193.59 |
‐ |
|||
Commercial code |
HOE |
C3D20 |
2 |
Hexa |
193.92 |
100.17% |
Commercial code |
LOE |
C3D8I |
1 |
Hexa |
193.58 |
99.99% |
Salome-Meca 2021 |
HOE |
3D |
2 |
Hexa |
193.93 |
100.17% |
Salome-Meca 2021 |
LOE |
3D |
1 |
Hexa |
197.19 |
101.86% |
Commercial code 2nd order elements (mode8)#
Commercial code 1st order elements (mode8)#
Salome-Meca 2019 2nd order elements (mode8)#
Salome-Meca 2019 1st order elements (mode8)#
Solver |
Pattern |
Type |
Order |
Shape |
Result |
Error |
|---|---|---|---|---|---|---|
Reference value |
1 |
206.19 |
‐ |
|||
Commercial code |
HOE |
C3D20 |
2 |
Hexa |
206.64 |
100.22% |
Commercial code |
LOE |
C3D8I |
1 |
Hexa |
200.13 |
97.06% |
Salome-Meca 2021 |
HOE |
3D |
2 |
Hexa |
206.64 |
100.22% |
Salome-Meca 2021 |
LOE |
3D |
1 |
Hexa |
210.55 |
102.11% |
Commercial code 2nd order elements (mode9&10)#
Commercial code 1st order elements (mode9&10)#
Salome-Meca 2019 2nd order elements (mode9&10)#
Salome-Meca 2019 1st order elements (mode9&10)#