4.4.5 FV16: Cantilevered thin square plate

Product: ABAQUS/Standard

Elements tested

S8R S8R5 STRI65

Problem description

Node	Coordinates
Numbers	x	y
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:

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
	1	2	3	4	5	6
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)