• Version
• 127 Downloads
• 2.28 MB File Size
• 1 File Count
• December 2, 2016 Create Date
• December 2, 2016 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - Stresses in and General Instability of Monocoque Cylinders with Cutouts - II - Calculation of the Stresses in a Cylinder with a Symmetric Cutout

A numerical procedure is presented for the calculation
of the stresses in a monochue cylinder with a cutout. In
the procedure the structure is broken up into a great many
units; the forces in these units corresponding to specified
distortions of the units are calculated; a set of linear
equations is established expressing the equilibrium con—
ditions of the units in the distorted state; and the
simultaneous linear equations are solved. A fully worked
out numerical example, corresponding to the applicatioh of
a pure bending moment, gave results in good agreement with
experiments carried out earlier at the Polytechnic Institute
of Brooklyn.

Actual airplanes differ greatly from the idealized
structures that underlie most theoretical analyses. The
reason for these deviations can be found in the great
difficulties involved in applying the theory of elasticity
to the irregular and complex structural parts of airplanes.
It is believed that the most promising approach to these
complex problems is the one in which the structure is
imagined to be broken up into a great number of “units,"
the forces in these units corresponding to specified dis—
tortions of the units are calculated, a set of linear
equations is established expressing the equilibrium con-
ditions of the units in the distorted state, and the
simultaneous linear equations are solved.

The set of linear equations, excluding the load terms,
forms what Southwell (reference 1) called the "operations
table." In Southwell's relaxation procedure the equations
are solved by a method of step—by—step approximations. In
the past 2 years a considerable amount of work has been done
at the Polytechnic Institute of Brooklyn in applying

Southwell's method to the stress analysis of reinforced thin—
walled structures. It was easily pOssible to establish a
rapidly converging rocedure in the case of stiffened panels
(references 2 and 5 . In the case of ring problems (refer~
ences 4 and 5) the convergence was found to be poor as a
rule, and suggestions were made for solving the equations
either directly by matrix methods, or by a procedure denoted
as the "growing unit“ method.