Products: ABAQUS/Standard ABAQUS/Explicit
Material and geometry specifications are as given in “Test 13: Simply supported thin square plate: frequency extraction,” Section 4.5.5.
Mesh:
A coarse mesh, a fine mesh, and a very fine mesh of a quarter of the plate are tested for elements S3R, S3RS, S4R, S4RS, and S4RSW in ABAQUS/Explicit. For the quadrilateral element types the mesh densities of the coarse, fine, and very fine meshes are 2 × 2, 3 × 3, and 4 × 4, respectively; for the triangular element types the mesh densities are 2 × 2 × 4, 3 × 3 × 4, and 4 × 4 × 4, respectively.
Forcing function:
Suddenly applied pressure.
100 N/m2 over whole plate.
Damping:
2% [2% of critical damping in the dominant first mode with analytical frequency value 
2.377 (Hz) or 
14.935 (sec–1)].
The damping factors are chosen as 
0.299 (sec–1) and 
1.339 × 10–3 (sec) so that
Response location:
and 
at center of plate.
Gauss integration is used for the shell cross-section in input file nft1358x.inp.
This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 13T from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.
The results are given in Table 4.5.7–1 through Table 4.5.7–6. The values enclosed in parentheses are percentage differences with respect to the reference solution. The static displacement was obtained by creating a second step with a time period of 23 seconds.
Table 4.5.7–1 Element type: S3R, ABAQUS/Explicit analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
 (mm) |  (sec) |  (N/mm2) |  (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Coarse mesh | 3.147 | 0.210 | 2.079 | 1.616 |
| (–10.67%) | (0.0%) | (–16.30%) | (–11.06%) | |
| Fine mesh | 3.313 | 0.210 | 2.207 | 1.701 |
| (–5.96%) | (0.0%) | (–11.15%) | (–6.38%) | |
| Very fine mesh | 3.370 | 0.210 | 2.239 | 1.732 |
| (–4.34%) | (0.0%) | (–9.86%) | (–4.68%) | |
Table 4.5.7–2 Element type: S3RS, ABAQUS/Explicit analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
| (mm) | (sec) | (N/mm2) | (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Coarse mesh | 3.263 | 0.210 | 2.028 | 1.679 |
| (–7.38%) | (0.0%) | (–18.36%) | (–7.59%) | |
| Fine mesh | 3.391 | 0.210 | 2.188 | 1.742 |
| (–3.75%) | (0.0% | (–11.92%) | (–4.13%) | |
| Very fine mesh | 3.429 | 0.210 | 2.244 | 1.762 |
| (–2.67%) | (0.0%) | (–9.66%) | (–3.01%) | |
Table 4.5.7–3 Element type: S4R, ABAQUS/Explicit analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
| (mm) | (sec) | (N/mm2) | (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Coarse mesh | 3.366 | 0.225 | 1.889 | 1.760 |
| (–4.46%) | (7.14%) | (–23.95%) | (–3.14%) | |
| Fine mesh | 3.414 | 0.215 | 2.105 | 1.756 |
| (–3.09%) | (2.38%) | (–15.26%) | (–3.36%) | |
| Very fine mesh | 3.427 | 0.215 | 2.186 | 1.762 |
| (–2.72%) | (2.38%) | (–12.00%) | (–3.03%) | |
Table 4.5.7–4 Element type: S4RS, ABAQUS/Explicit analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
| (mm) | (sec) | (N/mm2) | (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Coarse mesh | 3.495 | 0.240 | 1.974 | 1.797 |
| (–0.79%) | (14.3%) | (–20.53%) | (–1.1%) | |
| Fine mesh | 3.477 | 0.220 | 2.185 | 1.783 |
| (–1.31%) | (4.8%) | (–12.04%) | (–1.87%) | |
| Very fine mesh | 3.461 | 0.215 | 2.236 | 1.785 |
| (–1.76%) | (2.4%) | (–9.98%) | (–1.76%) | |
Table 4.5.7–5 Element type: S4RSW, ABAQUS/Explicit analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
| (mm) | (sec) | (N/mm2) | (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Coarse mesh | 2.486 | 0.205 | 1.400 | 1.759 |
| (–29.44%) | (–2.4%) | (–43.64%) | (–3.19%) | |
| Fine mesh | 3.254 | 0.215 | 2.015 | 1.759 |
| (–7.64%) | (2.4%) | (–18.88%) | (–3.19%) | |
| Very fine mesh | 3.395 | 0.215 | 2.181 | 1.774 |
| (–3.63%) | (2.4%) | (–12.20%) | (–2.24%) | |
Table 4.5.7–6 Element type: S8R5, ABAQUS/Standard analysis.
| Peak displacement | Peak stress | Static displacement | ||
|---|---|---|---|---|
| (mm) | (sec) | (N/mm2) | (mm) | |
| Reference solution | 3.523 | 0.210 | 2.484 | 1.817 |
| Direct solution | 3.467 (–1.59%) | 0.212 (0.95%) | 2.476 (–2.50%) | 1.780 (–2.04%) |
| Modal solution | 3.456 (–1.93%) | 0.214 (1.90%) | 2.426 (–2.33%) | 1.775 (2.37%) |
S3R elements, coarse mesh.
S3R elements, fine mesh.
S3R elements, very fine mesh.
S3RS elements, coarse mesh.
S3RS elements, fine mesh.
S3RS elements, very fine mesh.
S4R elements, coarse mesh.
S4R elements, fine mesh.
S4R elements, very fine mesh.
S4RS elements, coarse mesh.
S4RS elements, fine mesh.
S4RS elements, very fine mesh.
S4RSW elements, coarse mesh.
S4RSW elements, fine mesh.
S4RSW elements, very fine mesh.
S8R5 elements.
The modal solution in ABAQUS/Standard is obtained from Steps 3 and 4 in nfm1358x.inp.
