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C
(b)
B
Wrinkles in Square Membranes 119
Fig. 5. Wrinkled shapes for (a) T1 T /T2 T = 1and(b)T1 T /T2 T = 4.
Table 1.Wrinkles under symmetric loading (all values in mm)
n λ at r = 70 mm A
T (N) Eq. 21 Experiment Eq. 20 Experiment Eq. 22 Experiment
5 9.6 8 11.6 11.0 0.16 0.12
20 13.6 11 8.3 9.7 0.22 0.14
5 Validation of Analytical and Finite-Element Models
Table 1 compares the predicted wrinkle half-wavelengths and amplitudes from
Eqs. (20)–(22) with experimental measurements for a symmetrically loaded
membrane, i.e. for T1 T /T2 T =1.
For the load case T1 T /T2 T =4,Table 2 compares the analytical predictions
for the large diagonal wrinkle at the centre of the membrane, for two different
membrane thicknesses, with predictions from ABAQUS and experimental
measurements. The wavelength predictions are very close. The wrinkleamplitudes
have been estimated first using only analytical solutions, Eq. (24) with
δ1 and δ2 from Eq. (25), and second using Eq. (24) but with corner deflections
from a 2-D IMP analysis. We can see that the fully analytical estimates are up
to 88% higher than those measured experimentally, but if we use the corner
displacements from the 2D finite-element analysis we obtain estimates that
are only 48% and 16% higher than the measurements.
(a)
A
C
B
A