FV16: Cantilevered 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

S8R

S8R5

STRI65

Problem description



NodeCoordinates
Numbersxy
1 4.00 4.00
2 2.25 2.25
3 4.75 2.50
4 7.25 2.75
5 7.50 4.75
6 7.75 7.25
7 5.25 7.25
8 2.25 7.25
9 2.50 4.75

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=uz=ϕy=0 along the y-axis.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV16 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

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
123456
NAFEMS 0.421 1.029 2.582 3.306 3.753 6.555
STRI65 (Test 1) 0.418 (−0.71) 1.035 (0.58) 2.565 (−0.66) 3.325 (0.57) 3.870 (3.12) 6.966 (6.27)
STRI65 (Test 2) 0.420 (−0.24) 1.034 (0.49) 2.570 (−0.46) 3.326 (0.60) 3.850 (2.58) 6.843 (4.39)
S8R 0.491 1.025 2.583 3.330 3.742 7.278
(Test 1) (−0.48) (−0.39) (0.04) (0.73) (−0.29) (11.03)
S8R 0.423 1.044 2.634 3.345 4.105 7.048
(Test 2) (0.48) (1.46) (2.01) (1.18) (9.38) (7.52)
S8R 0.419 1.028 2.702 3.429 3.941 6.696
(Test 3) (−0.48) (−0.10) (4.65) (3.72) (5.01) (2.15)
S8R 0.420 1.049 2.707 3.723 4.128 7.008
(Test 4) (−0.24) (1.94) (4.84) (12.58) (9.99) (6.91)
S8R5 (Test 1) 0.418 (−0.71) 1.023 (−0.58) 2.569 (−0.50) 3.282 (−0.73) 3.721 (−0.85) 5.988 (−8.65)
S8R5 (Test 2) 0.418 (−0.71) 1.024 (−0.49) 2.569 (−0.50) 3.283 (−0.70) 3.722 (−0.83) 6.077 (−7.29)
S8R5 (Test 3) 0.418 (−0.71) 1.021 (−0.78) 2.661 (3.06) 3.382 (2.30) 3.946 (5.14) 6.814 (3.95)
S8R5 (Test 4) 0.419 (0.24) 1.022 (−0.68) 2.630 (1.86) 3.560 (1.63) 3.920 (4.45) 6.602 (0.72)