Elements tested
CAX4
CAX8
CAX6
CAX6M
FV42: Thick hollow sphere: uniform radial vibration | ||
| ||
ProductsAbaqus/Standard
Problem description
Model:
Shell thickness = 4.2 m.
Material:
Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.
Boundary conditions:
Unsupported.
Reference solution
This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV42 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.
Radial displacement; Mode shapes predicted by Abaqus (for element type CAX8)
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 | |
| NAFEMS | 369.91 | 838.03 | 1451.2 | 2111.7 | 2795.8 |
| CAX4 | 367.79 (−0.03) | 829.11 (−1.06) | 1417.6 (−2.32) | 2025.8 (−4.07) | 2598.4 (7.60) |
| CAX8 | 370.97 (0.29) | 840.49 (0.29) | 1457.3 (0.42) | 2137.9 (0.99) | 2861.1 (2.33) |
| CAX6 | 369.95 (0.01) | 838.04 (0.00) | 1451.3 (0.00) | 2118.0 (0.30) | 2800.2 (0.16) |
| CAX6M | 370.06 (0.04) | 836.50 (−0.18) | 1443.0 (−0.57) | 2092.1 (−0.93) | 2738.8 (−2.04) |
Input files
- nfv4264f.inp
-
CAX4 elements.
- nfv4268c.inp
-
CAX8 elements.
- nfv4266c.inp
-
CAX6 elements.
- nfv4266m.inp
-
CAX6M elements.