4.4.9 FV42: Thick hollow sphere: uniform radial vibration

Product: ABAQUS/Standard  

Elements tested

CAX4    CAX8    CAX6    CAX6M   

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
12345
NAFEMS369.91838.031451.22111.72795.8
CAX4367.79 (–0.03)829.11 (–1.06)1417.6 (–2.32)2025.8 (–4.07)2598.4 (7.60)
CAX8370.97 (0.29)840.49 (0.29)1457.3 (0.42)2137.9 (0.99)2861.1 (2.33)
CAX6369.95 (0.01)838.04 (0.00)1451.3 (0.00)2118.0 (0.30)2800.2 (0.16)
CAX6M370.06 (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.