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National Advisory Committee for Aeronautics, Technical Notes - Deflection and Stress Analysis of Thin Solid Wings of Arbitrary Plan Form with Particular Reference to Delta Wings

The structural analysis of arbitrary solid cantilever wings by
small—deflection.thin-plate theory is reduced to the solution of linear
ordinary differential equations by the assumption that the chordwise
deflections at any spanwise station may be expressed in the form of a
power series in.which the coefficients are functions of the spanwise
coordinate. If the Series is limited to the first two and three terms
(that is, if linear and parabolic chordwise deflections, respectively,
are assumed), the differential equations for the coefficients are solved
exactly for.uniformly loaded solid delta wings of constant thickness and
of diamond chordwise cross section with constant thickness ratio. For
cases for which exact solutions to the differential equations cannot be
obtained, a numerical procedure is derived. Experimental deflection
and stress data for constant- thickness delta—plate specimens of 45°
and 60° sweep are presented and are found to compare favorably with the
present theory.

One of the present trends in the development of high-speed air—
planes and missiles is toward the use of thin low-aspect-ratio wings.
The structural analysis of these wings often cannot be based on beam
theory since the structural deformations may vary considerably from
those of a beam and, indeed, may more closely approach those of a plate.
In cases Where the wing construction is solid or nearly solid the.use of
plate theory in the analysis is particularly valid, and it is this type
of wing which is considered in the present paper.

Exact solutions to the partial-differential equation of plate
theory are not readily obtained, especially for plates of arbitrary
shape and loading; however, a number of approximate solutions to
specific problems on cantilever plates have appeared in the literature
(see, for example, references 1 to 7). Of the approaches used in these
references, only the one in references 6 and 7 is readily applicable to
plates of arbitrary plan form, thickness distribution, and load distri-
bution; thus it is the most useful one f0r_the analysis of actual wings.