Charts Giving Critical Compressive Stress of Continuous Flat Sheet Divided Into Parallelogram-Shaped Panels Page: 10 of 32
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NACA TN 2392
In the sketch, the buckle pattern is represented as being sym-
metrical about a panel midpoint and repeating in every panel. However,
in general, a repetitive buckle pattern can be assumed to take place
in a group of panels of unknown dimensions Na in the x-direction and
Nb' in the y'-direction, where N and M are integers.
A representation of such a pattern can be built up in two steps.
First, zero deflection along all panel boundaries can be provided by
= sin sin (Al)
1 Na Mb'
where the ratios p/N and q/M are integers. For stress in the
y-direction, equation (Al) with = 1 and M= 1, 2, 3, is a
suitable approximation for the buckle pattern which occurs over a wide
range of panel aspect ratio and skew angle 6. Similarly, the buckle
pattern occurring in slightly skewed panels of moderate aspect ratio
under stress in the x-direction is represented by equation (Al) with
= , 2,3,. . . and -= . For this special case, the nodal
lines a-a in the sketch are parallel to the y'-direction. In order to
represent all other orientations of the nodal lines a-a and to permit
an arbitrary uniform spacing, w1 can be multiplied by some function
such as w2, where
w2=cosY. ' : (A2)
The lines along which w2 = 0 have a slope determined by the
ratio Na/Mb' and a spacing determined by the ratio j/N, where j
is an integer and may take on all values 0, 1, 2, 3, . . .
By multiplying wl by w2, the desired deflection function
w = sin ' sin y' cos x NNa Y (A3)
Na Mb' Na Mb'
is obtained. This function is capable of satisfying the idealized
physical characteristics of the buckle pattern for any panel aspect
ratio and skew angle upon proper choice of the integers p, q, N, MN
and J. Actually, it is necessary to consider only the plus sign in
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Anderson, Roger A. Charts Giving Critical Compressive Stress of Continuous Flat Sheet Divided Into Parallelogram-Shaped Panels, report, July 1951; (https://digital.library.unt.edu/ark:/67531/metadc59839/m1/10/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.