FV41: Free cylinder: axisymmetric vibration

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

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
NAFEMS RBM 243.53 377.41 394.11 397.72 405.28
CAX4 RBM 243.05 (−0.20) 368.41 (−2.38) 378.05 (−4.08) 384.00 (−3.45) 389.02 (−4.01)
CAX4I RBM 243.17 (−0.15) 370.80 (−1.75)) 379.28 (−3.76) 385.92 (−2.06) 389.54 (−3.88)
CAX6 RBM 243.50 (−0.01) 377.41 (0.00) 394.26 (0.04) 397.90 (0.05) 406.42 (0.28)
CAX6M RBM 243.37 (−0.07) 376.19 (−0.32) 392.80 (−0.33) 394.48 (−0.81) 399.76 (−1.36)
CAX8 RBM 243.50 (−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.