FV52: Simply supported “solid” 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

C3D8I

C3D10

C3D10HS

C3D10M

C3D20

Problem description



Model:

Plate thickness = 1.0 m.

Material:

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

Boundary conditions:

uz=0 along all four edges on the plane z =−0.5.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV52 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by Abaqus (for element type C3D8I)

The following 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, 345678910
NAFEMS RBM 44.092 106.66 106.66 156.23 193.58 200.13 200.13
C3D8I RBM 44.092 (0.0) 106.66 (0.0) 106.66 (0.0) 156.23 (0.0) 193.58 (0.0) 200.13 (0.0) 200.13 (0.0)
C3D10 RBM 44.348 (0.58) 107.73 (1.00) 107.73 (1.00) 163.58 (4.70) 193.63 (0.02) 204.74 (2.30) 205.10 (2.48)
C3D10HS RBM 44.348 (0.58) 107.73 (1.00) 107.73 (1.00) 163.58 (4.70) 193.63 (0.02) 204.74 (2.30) 205.10 (2.48)
C3D10M RBM 42.687 (−3.19) 101.57 (−4.77) 101.57 (−4.77) 151.22 (−3.21) 192.89 (−0.35) (Mode 10) 203.76 (1.81) (Mode 11) 203.76 (1.81) (Mode 12)
C3D20 RBM 44.796 (1.60) 110.54 (3.64) 110.54 (3.64) 169.10 (8.24) 193.92 (0.18) 206.64 (3.25) 206.64 (3.25)

Remarks

Element types C3D10, C3D10M, and C3D20 capture the same eigenmodes, but the order of eigenmodes 8 through 12 is different. For example, the same mode is captured as mode 12 by C3D10, as mode 11 by C3D10M, and as mode 9 by C3D20. Element type C3D8I captures the eigenmodes in the same order as C3D20.