Test 21: Simply supported thick square plate: frequency extraction

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

S4

S4R

S4R5

S8R

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. uz=0 along all four edges. ϕx=0 along edges x=0 and x=10, ϕy=0 along edges y=0 and y=10.

Frequency extraction is performed in Step 1.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 21 from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.

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 given in Table 1 through Table 4.

Table 1. Element type: S4.
ModeAbaqus resultNAFEMS reference result% Difference
1  46.667 45.897 1.68
2, 3 115.92 109.41 5.95
4 178.00 167.89 6.02 
5, 6 233.73 204.51 14.28
7, 8 285.20 256.50 11.19
Table 2. Element type: S4R.
ModeAbaqus resultNAFEMS reference result% Difference
1 46.485 45.897 1.28
2, 3 115.24 109.41 5.33
4 175.47 167.89 4.51
5, 6 232.39 204.51 13.63
7, 8 280.08 256.50 9.19
Table 3. Element type: S4R5.
ModeAbaqus resultNAFEMS reference result% Difference
1 46.514 45.897 1.34
2, 3 115.55 109.41 5.61
4 177.26 167.89 −5.29
5, 6 233.66 204.51 14.25
7, 8 285.99 256.50 11.48
Table 4. Element type: S8R.
ModeAbaqus resultNAFEMS reference result% Difference
1 45.936 45.897 0.08
2, 3 110.41 109.41 0.91
4 170.38 167.89 1.48
5, 6 212.81 204.51 4.06
7, 8 269.96 256.50 5.25