4.4.8 FV41: Free cylinder: axisymmetric vibration

Product: ABAQUS/Standard  

Elements tested

CAX4    CAX4I    CAX6    CAX6M    CAX8   

Problem description

Model:

Wall thickness = 0.4 m.

Material:

Young's modulus = 200 GPa, Poisson's ration = 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 FV41 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by ABAQUS

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
NAFEMSRBM243.53377.41394.11397.72405.28
CAX4RBM243.05 (–0.20)368.41 (–2.38)378.05 (–4.08)384.00 (–3.45)389.02 (–4.01)
CAX4IRBM243.17 (–0.15)370.80 (–1.75))379.28 (–3.76)385.92 (–2.06)389.54 (–3.88)
CAX6RBM243.50 (–0.01)377.41 (0.00)394.26 (0.04)397.90 (0.05)406.42 (0.28)
CAX6MRBM243.37 (–0.07)376.19 (–0.32)392.80 (–0.33)394.48 (–0.81)399.76 (–1.36)
CAX8RBM243.50 (–0.01)377.46 (0.01)394.30 (0.05)397.97 (0.06)406.44 (0.29)

Remarks

In comparison to element types CAX6 and CAX8, element types CAX4, CAX4I, and CAX6M require a greater mesh refinement to capture the higher modes accurately.

Input files

nfv41f4f.inp

CAX4 elements.

nfv41i4f.inp

CAX4I elements.

nfv41f6f.inp

CAX6 elements.

nfv41m6f.inp

CAX6M elements.

nfv41f8c.inp

CAX8 elements.