Although the problem of the stability of a fuselage that is subjected to
torsional force is important in connection with the case of light metal
construction of an aeroplane in flight, the theoretical side of the problem
does not seem to have received much attention. This is probably because of
the difficulty of obtaining its mathematical solution even in the case where
the fuselage is assumed to be a circular hollow cylinder.
Thus, I studied the problem in assuming that the fuselage is a cylindrical
shell for the first approximation. Southwell and Skan have dealt with the
stability of a plane elastic strip due to edge shearing forces, but their
result cannot be applied to the problem of the cylindrical shell unless its
length is very short. Schwerin seems to be the only one who has written on
the torsional stability of a cylindrical shell. Although his method of
constructing the differential equations of the equilibrium of a cylindrical
shell has been chiefly derived from Love's text book, and appears correct in
the main, yet owing to the certain apparent particularities on his part his
solutions of equations are open to grave doubts.