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A problem arises how to estimate a value of the bifurcation shortening for the real structure, in
which inevitable geometrical imperfections are embodied. In this case, an effect of bifurcation is not
observed and it is impossible to define directly a value of the bifurcation shortening. In the present
study, a methodology for determination of an approximate value of the bifurcation shortening for
the real thin-walled column under compression has been developed, employing an axial shorteningsquared
deflection amplitude plot. It has been shown that the applied method can determine the
bifurcation shortening with satisfactory accuracy. The obtained results have been compared to the
FEM results. Detailed calculations have been conducted for short angle columns. The eigenvalue
problem and the nonlinear post-buckling problem have been solved with the perturbation method based
on Byskov-Hutchinson’s method and the finite element method using an Abaqus software package.
The axial shortening - squared deflection amplitude plots have been determined and an effect of the
imperfection amplitude on the post-buckling behaviour of laminated thin-walled angle columns has been
analysed. General configurations of the laminate plies have been selected. All columns have been simply
supported at both ends. Because of the computations conducted, it has been found that a value of the
shortening corresponding to the bifurcation shortening of the real laminated thin-walled structure can
be determined from the shortening - squared deflection amplitude plot, assuming that the post-buckling
state is described with a linear relationship on this plot, whereas the value of the bifurcation shortening
corresponds to a free term of the straight line approximating the post-buckling mode on the plot. The proposed procedure has been positively verified with the finite element method. The presented method
based on the shortening-squared deflection amplitude plot underestimates the bifurcation shortening
and the error does not exceed several percent for all cases. If an amplitude of initial deflections is very
low, the error is the lowest and does not exceed 1.5%. An increase in the initial deflection amplitude is
followed by a quick increase in the error up to a few percent. A further increase in the initial deflection
amplitude does not result in a fast growth of the error. Comparing all the results, one can state that
the proposed method enables estimation of the bifurcation shortening with a high accuracy in a broad
range of initial deflection amplitudes in the case of real structures. The proposed method is by far more
accurate than the already known methods. In all cases of the initial deflection amplitude, the error is
acceptable and it is less than 12.3%. In the case of the load-shortening method or the load - squared
deflection method, the estimation error of the bifurcation load is twice as high, whereas an application
of the intersection method causes that the error grows sharply and it is four times higher.
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