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This study investigated the problem of the global stability of hybrid FGM-FML and laminated columns
with different layups, considering many coupling effects of the stiffness submatrix. The lowest eigenvalues
were determined by 4 methods. The first two are analytical beam methods (i.e. 1D modelling
approaches) based on the use of the Euler-Bernoulli theory. The third is an analytical-numerical ANM
perturbation method based on Koiter’s theory (i.e. 2D plate modelling), and the fourth method is the
FEM (3D shell approach) which is used for the verification of the previous calculations. Method 1 for
1D was based on the longitudinal flexural stiffness of the column and load reduction into the centre
of stiffness of the cross section. Method 2 for 1D used the inverse stiffness matrix, or the longitudinal
flexural flexibility. The 3 ANM method was based on Koiter’s theory for thin-walled plates, or 2D.
Compressed thin-walled structures usually fail due to loss of stability. This can encompass various types
of phenomena, i.e. global buckling, interaction buckling or distortional buckling. Local buckling, which
does not lead to failure but can significantly reduce the load carrying capacity of a thin-walled structure
because of its interaction with another buckling mode, should also be considered in the column design.
In slender structures, the global buckling mode caused failure. Because of practical aspects, particularly
the specific mechanical characteristics of the thin-walled structures under study, it seems reasonable to
ask whether their behaviour must be described using the general shell or plate theories. In practical
applications, the finite element method can be used. For selected cases too, a simple beam model
could be developed in accordance with the Euler-Bernoulli theory in order to accurately estimate the
lowest eigenvalue load. The ease of calculations by the beam model makes it possible in engineering
applications to effectively optimize compressed thin-walled structures exposed to loss of stability. Hybrid
multi-ply prismatic columns and a rectangular cross section were investigated in the study. Each ply was
made of different materials satisfying Hooke’s law. The Euler-Bernoulli beam theory for conservative
systems was adopted. The columns were slender, simply supported and subjected to uniform compression
in the elastic range. The x-axis direction describing the length of the column did not necessarily
have to coincide with the orientation of the reinforcing fibres in the glass/carbon fibre-reinforced plastics
(GFRP, CFRP). From the classical laminated plate theory (CLPT) directly followed the constitutive
relationships and expressions for the stiffness and flexibility matrices. Local buckling of the column was
omitted. Very good agreement was obtained for the 50 cases of columns analysed using Methods 2-4,
while for Method 1 the largest error was unacceptable as it exceeded 250%. Given the ease of obtaining
solutions, it is recommended using Method 2 (1D model) because it yields results that are as accurate
as those produced with the much more labour-consuming Methods 3-4 (2D and 3D models). The
investigations of Andrzej Teter were financed within the Lublin University of Technology – contract no.
M/KMS/FD-20/M-5/122/2022.
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