Test 21H: Simply supported thick 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

Problem description

Material and geometry specifications are as given in Test 21: Simply supported thick square plate: frequency extraction.

Forcing function

Steady-state harmonic.

F=F0 sin⁡(ω⁢t)

F0=​ 1 MN/m2 over whole plate.

ω=2⁢π⁢f

f=​ 0 to 78.17 Hz

Damping

ζ=​ 2%

Response

uz and σ11 at center of plate.

The modal solution is obtained from Step 2 in files whose names begin with nfm21.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 21H 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.

Table 1. Modal solution.
 Peak displacement (mm)Peak stress (N/mm2)Frequency (Hz)
Reference solution 58.33 800.8 45.90
S4 59.54 (2.03%) 784.01 (−2.09%) 46.67(1.68%)
S4R 60.01 (2.88%) 760.4 (−5.04%) 46.52 (1.35%)
S4R5 59.93 (2.74%) 760.8 (−5.00%) 46.51 (1.33%)
S8R 59.94 (2.76%) 880.1 (9.90%) 45.94 (0.09%)
Table 2. Direct solution.
 Peak displacement (mm)Peak stress (N/mm2)Frequency (Hz)
Reference solution 58.33 800.8 45.90
S3/S3R 57.52 (−1.39%) 745.7 (−6.88%) 47.92 (4.40%)
S4R (collapsed) 57.52 (−1.39%) 745.7 (−6.88%) 47.92 (4.40%)
S4 (collapsed) 57.52 (−1.39%) 745.7 (−6.88%) 47.92 (4.40%)
S4 60.77 (4.18%) 800.3 (−0.06%) 46.76(1.87%)
S4R 61.33 (5.14%) 776.9 (−2.98%) 46.39 (1.07%)
S4R5 61.09 (4.73%) 775.7 (−3.13%) 45.98 (0.17%)
S8R 61.87 (6.07%) 908.4 (13.44%) 45.98 (0.17%)
S8R5 60.81 (4.25%) 887.8 (10.8%) 46.0 (0.22%)
S9R5 60.73 (4.11%) 830.3 (3.68%) 46.0 (0.22%)
STRI3 55.88 (−4.20%) 818.4 (2.19%) 46.8 (1.96%)
STRI65 62.47 (7.09%) 860.7 (7.48%) 46.0 (0.22%)