Elements tested
CSS8
S3R
S4
S4R
S4R5
S8R
STRI65
SC6R
SC8R
FV12: Free thin square plate | ||
| ||
ProductsAbaqus/Standard
Problem description
Model:
Plate thickness = 0.05 m.
Material:
Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.
Boundary conditions:
at all nodes. The continuum shell meshes use equation constraints to provide equivalent midsurface kinematic constraints.
Reference solution
This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV12 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.
Mode shapes predicted by Abaqus (for element type S4R5)
The contour plots were generated by setting the maximum and minimum contour levels close to zero. Where contour levels coincided with the element boundaries, the maximum contour level was increased and the minimum contour level was decreased appropriately.
Results and discussion
The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.
| Mode | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1, 2, 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| NAFEMS | RBM | 1.622 | 2.360 | 2.922 | 4.233 | 4.233 | 7.416 | N/A |
| S3R | RBM | 1.64 (1.1) | 2.40 (1.7) | 3.00 (2.7) | 4.38 (3.5) | 4.47 (5.6) | 7.98 (7.6) | 7.98 |
| S4 | RBM | 1.633 (0.68) | 2.403 (1.82) | 3.007 (2.91) | 4.286 (1.25) | 4.286 (1.25) | 7.973 (7.55) | 8.032 |
| S4R | RBM | 1.631 (0.55) | 2.403 (1.82) | 3.007 (2.91) | 4.265 (0.76) | 4.265 (0.76) | 7.880 (6.26) | 8.028 |
| S4R5 | RBM | 1.622 (0.00) | 2.362 (0.08) | 2.931 (0.31) | 4.131 (−2.41) | 4.131 (−2.41) | 7.875 (6.19) | 7.875 |
| S8R | RBM | 1.626 (0.25) | 2.369 (0.38) | 2.935 (0.44) | 4.185 (−1.13) | 4.185 (−1.13) | 7.559 (1.93) | 7.559 |
| STR165 (2×4×4 mesh) | RBM | 1.628 (0.37) | 2.364 (0.17) | 2.931 (0.31) | 4.229 (−0.09) | 4.265 (−0.76) | 7.490 (1.00) | 7.533 |
| SC6R | RBM | 1.644 (1.4) | 2.4 (1.7) | 3.0 (2.7) | 4.3 (1.6) | 4.47 (5.6) | 7.97 (7.7) | 7.98 |
| SC8R | RBM | 1.63 (0.5) | 2.4 (1.7) | 3.0 (2.7) | 4.26 (0.6) | 4.26 (0.6) | 7.8 (6.1) | 8.02 |
| SC8R* | RBM | 1.635 (0.8) | 2.403 (1.8) | 3.008 (2.9) | 4.308 (1.7) | 4.308 (1.7) | 8.037 (8.3) | 8.037 |
| CSS8 | RBM | 1.587 (2.2) | 2.253 (4.5) | 2.830 (3.1) | 3.974 (6.1) | 3.974 (6.1) | 7.024 (5.3) | 7.416 |
| *Abaqus/Standard results with enhanced hourglass control. | ||||||||
Input files
- nfv12_std_s3r.inp
-
S3R elements.
- nfv12e4x.inp
-
S4 elements.
- nfv12f4x.inp
-
S4R elements.
- nfv1254x.inp
-
S4R5 elements.
- nfv1268x.inp
-
S8R elements.
- nfv1256x.inp
-
STRI65 elements.
- nfv12_std_sc6r.inp
-
SC6R elements.
- nfv12_std_sc8r.inp
-
SC8R elements.
- nfv12_std_sc8r_eh.inp
-
SC8R elements with enhanced hourglass control.
- nfv12_std_css8.inp
-
CSS8 elements.