Compressive and Torsional Buckling of Thin-Wall Cylinders in Yield Region Page: 3 of 43

                                
NACA TN 3726

Investigator      Stress-strain law  Plasticity law Buckling model
Bijlaard             Incremental and       Octahedral     No strain
(ref. 2)            deformation types,     shear          reversal
v instantaneous
Ilyushin             Deformation type,     Octahedral     Strain
(ref. 3)           . v = 0.5               shear          reversal
Handelman and Prager Incremental type,     Octahedral     Strain
(ref. 4)            v instantaneous        shear          reversal
Stowell             Deformation type,      Octahedral     No strain
(refs. 5 and 6)      v = 0.5               shear          reversal
Historically, Bij1aard (ref,. 2) appears to have been the first to
arrive at satisfactory theoretical solutions for inelastic-buckling
theories. His work is the most comprehensive of all those considered
in that he considers both incremental and deformation theories and con-
cludes that the deformation type is correct since it leads to lower
inelastic buckling loads than those obtained from incremental theories.
His work was first published in 1937. That paper and later publications
include solutions to many important inelastic-buckling problems. How-
ever, this work appears to have remained unknown to most of the later
investigators .
flyushin (ref. 3) briefly referred to Bijlaard's work and then pro-
ceeded to derive the basic differential equation for inelastic buckling
of flat plates according to the strain-reversal model. The derivation
of this equation is rather elegant and was used by Stowell (ref. 5), who,
however, used the no-strain-reversal model. The differential equation
obtained by Bijlaard reduces to that derived by Stowell by setting
v = 1/2  in the former. Handelman and Prager (ref. 4), during this time,
obtained solutions to several inelastic-buckling problems by use of
incremental theory. Test data on compressed flanges and plates indicate
that the results of incremental theories are definitely unconservative
regardless of the buckling model, whereas deformation-type theories are
in relatively good agreement.
The problem of plastic buckling has also been the subject of much
experimental research. The use of the secant-modulus-reduction factor
was first proposed for plates under compressive loads by Gerard (ref. 7)
on the basis of tests on Z- and channel sections. Later, Stowell (ref. 5)
proved theoretically that use of the secant modulus is correct for hinged.
flanges and that for elastically restrained flanges and plates the