FV2: Pin-ended double cross: in-plane 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

B22

B23

Problem description



Material:

Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.

Boundary conditions:

Beams are pinned at A, B, C, D, E, F, G, H.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV2 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by Abaqus



Modes 2 through 8 are vibration modes with the same eigenvalues. Because the eigenvalues are identical, any linear combination of modes 2 through 8 is still a valid mode. Hence, the shapes of these modes are arbitrary linear combinations of the mode shapes shown in the figure, and in particular will vary from computer to computer. The same behavior is observed for modes 10 through 16.

Results and discussion

The results are shown in Table 1 and Table 2. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Table 1. B22 and B23 Modes 1–8 element results.
 Mode
12345678
NAFEMS 11.336 17.709 17.709 17.709 17.709 17.709 17.709 17.709
B22 11.337 (0.01) 17.676 (−0.19) 17.676 (−0.19) 17.699 (−0.06) 17.706 (−0.02) 17.707 (−0.01) 17.707 (−0.01) 17.712 (0.02)
B23 11.343 (0.06) 17.697 (−0.07) 17.697 (−0.07) 17.721 (0.07) 17.721 (0.07) 17.728 (0.11) 17.728 (0.11) 17.733 (0.14)
Table 2. B22 and B23 Modes 9–16 element results.
 Mode
910111213141516
NAFEMS 45.345 57.390 57.390 57.390 57.390 57.390 57.390 57.390
B22 45.686 (0.75) 57.745 (0.62) 57.745 (0.62) 58.059 (1.17) 58.080 (1.20) 58.081 (1.20) 58.081 (1.20) 58.101 (1.24)
B23 45.544 (0.44) 57.457 (0.12) 57.457 (0.12) 57.759 (0.64) 58.780 (2.42) 58.781 (2.42) 58.781 (2.42) 58.801 (2.46)