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National Advisory Committee for Aeronautics, Technical Notes - Equivalent Plate Theory for a Straight Multicel Wing

A structural theory is developed for the analysis of thin multi-
cell wings with straight spars and perpendicular ribs. The analysis
is intended to be suitable for supersonic wings of low aspect ratio.
Deflections due to shearing strains are taken into account. The theory
is expressed entirely in terms of first-order difference equations in
order that analogous electrical circuits can'be readily designed and
solutions obtained on the Cal—Tech analog computer.

In the process of designing thin supersonic wings for minimum
weight it is found that a convenient construction with aluminum alloy
consists of a rather thick skin with closely spaced spars and no stringers.
Such a wing deflects in the manner of a plate rather than as a beam.
Internal stress distributions may be considerably different from those
given by beam theory, particularly for torsional or eccentric loading.

A thin-walled multicell wing may be regarded as an elastic shell
in which the webs, or wall segments, act as membranes. By introducing
appropriate simplifying assumptions it is possible to reduce the equa-
tions for such a shell to the form of plate equations provided that one
simple criterion is satisfied. The chordwise cross sections must have
a horizontal axis of symmetry. This condition is usually satisfied in
supersonic wings which do not contain stringers.

The theory which has been developed is of the simplest form that
could be reasonably expected to give results of an accuracy that would
be satisfactory for engineering purposes. The loading is assumed to
consist of a set of vertical concentrated forces acting at the inter-
sections of the ribs and spars. The distributed load on the wing must
be replaced, in some rational manner, by an equivalent set of concen-
trated loads.

In order that a solution may be obtained on an analog computer,
the structural theory is expressed entirely in terms of first-order
difference equations. The design of the analogous electrical circuit
is explained and illustrated.