FV12: Free thin square plate

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

CSS8

S3R

S4

S4R

S4R5

S8R

STRI65

SC6R

SC8R

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:

ux=uy=ϕz=0 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.