FV22: Clamped thick rhombic 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

S3R

S4

S4R

S8R

SC6R

SC8R

Problem description



Model:

Plate thickness = 1.0 m.

Material:

Young's modulus = 200 GPa, Poisson's ration = 0.3, density = 8000 kg/m3.

Boundary conditions:

ux=uy=ϕz=0 at all nodes. vz=ϕx=ϕy=0 along all edges. 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 FV22 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by Abaqus



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
NAFEMS 133.95 201.41 265.81 282.74 334.45 N.A.
S3R 143.11 (6.8) 232.33 (15.4) 307.61 (15.7) 333.37 (17.9) 446.63 (33.6) 456.72
S4 136.50 (1.9) 215.60 (7.04) 292.01 (9.86) 295.96 (4.68) 380.96 (13.91) 423.86
S4R 135.50 (1.16) 213.61 (6.06) 287.25 (8.07) 293.99 (3.98) 372.50 (11.38) 421.20
S8R 132.28 (1.25) 199.67 (0.86) 265.78 (0.01) 281.67 (0.38) 338.72 (1.28) 382.09
SC6R 144.18 (7.6) 235.09 (16.7) 312.44 (17.5) 338.54 (19.7) 455.64 (36.2) 465.54
SC8R 136.44 (1.9) 216.00 (7.2) 291.27 (9.58) 298.43 (5.5) 378.66 (13.2) 429.43