4.5.9 Test 21: Simply supported thick square plate: frequency extraction

Product: ABAQUS/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:

at all nodes. along all four edges. along edges and , along edges and .

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 4.5.9–1 through Table 4.5.9–4.

Table 4.5.9–1 Element type: S4.

Mode	ABAQUS result	NAFEMS 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 4.5.9–2 Element type: S4R.

Mode	ABAQUS result	NAFEMS 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 4.5.9–3 Element type: S4R5.

Mode	ABAQUS result	NAFEMS 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 4.5.9–4 Element type: S8R.

Mode	ABAQUS result	NAFEMS 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

Input files

S4 elements.

S4R elements.

S4R5 elements.

S8R elements.