Test 13H: Simply supported thin square plate: harmonic forced 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

  • S3
  • S3R
  • S4
  • S4R
  • S4R5
  • S8R
  • S8R5
  • S9R5
  • STRI3
  • STRI65
  • SC6R
  • SC8R

Problem description

Material and geometry specifications are as given in Test 13: Simply supported thin square plate: frequency extraction.

Forcing function

Steady-state harmonic.

F=F0 sin⁡(ω⁢t)

F0=​ 100 N/m2 over whole plate.

ω=2⁢π⁢f

f=​ 0 to 4.16 Hz

Damping

ζ=​ 2%

Response

uz and σ11 at center of plate.

General:

Gauss integration is used for the shell cross-section in input file nfh1368x.inp.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 13H from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.

Response predicted by Abaqus



Results and discussion

The results are given in Table 1 and Table 2. The values enclosed in parentheses are percentage differences with respect to the reference solution. The modal solutions are obtained from Step 2 in files whose names begin with nfm13.

Table 1. Modal solution.
 Peak displacement (mm)Peak stress (N/mm2)Frequency (Hz)
Reference solution 45.42 30.03 2.377
S4 45.03 (−0.85%) 31.33 (4.3%) 2.418 (−1.72%)
S4R 45.33 (−0.20%) 30.34 (1.03%) 2.410 (1.39%)
S4R5 45.42 (0.00%) 30.41 (1.27%) 2.407 (1.26%)
S8R 43.12 (−5.06%) 33.73 (12.32%) 2.441 (2.69%)
S8R5 45.50 (0.18%) 35.12 (16.95%) 2.377 (0.00%)
Table 2. Direct solution.
 Peak displacement (mm)Peak stress (N/mm2)Frequency (Hz)
Reference solution 45.42 30.03 2.377
S3/S3R 41.56 (−8.50%) 27.82 (−7.36%) 2.49 (4.75%)
S4 44.93 (−1.08%) 31.26 (4.10%) 2.420 (1.81%)
S4 (collapsed) 41.56 (−8.50%) 27.82 (−7.36%) 2.49 (4.75%)
S4R 45.38 (−0.09%) 30.37 (1.13%) 2.405 (1.18%)
S4R (collapsed) 41.56 (−8.50%) 27.82 (−7.36%) 2.49 (4.75%)
S4R5 45.41 (−0.02%) 30.39 (1.20%) 2.405 (1.18%)
S8R 43.86 (−3.43%) 34.31 (14.25%) 2.446 (2.90%)
S8R5 44.66 (−1.34%) 34.49 (14.85%) 2.385 (0.34%)
S9R5 44.59 (−1.83%) 32.24 (7.36%) 2.39 (0.55%)
STRI3 44.74 (−1.49%) 32.81 (9.26%) 2.36 (−0.71%)
STRI65 44.96 (−1.01%) 33.19 (10.5%) 2.36 (−0.71%)
SC6R 41.56 (−8.5%) 27.82 (−7.36) 2.49 (4.75%)
SC8R 45.38 (−0.09%) 30.37 (1.13%)  2.405 (1.18%)