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A multimodal approach to the phenomenon of buckling of thin[U+2010]walled columns made of
laminate with local isotropic stiffeners in the elastic range was applied. Numerical simulations were
conducted with two methods: the perturbation method based on Koiter’s theory (i.e. semi-analytical
method SAM) and the finite element method. The structures under analysis were simply supported
at both ends and subjected to uniform compression. Numerical models using FEM were built withthe Abaqus system. In the FEM model, second-order four-node shell elements with eight degrees of
freedom in each node (S8R-type element) were applied. A nonlinear problem was solved with the Riks
algorithm to trace stable and unstable equilibrium paths. Dimensions of the structures were selected
to make the eigenvalues close, and thus to ensure a very strong interaction between the modes. In
the perturbation method based on Koiter’s theory, it was possible to consider a precisely defined and
finite number of buckling modes, considering in the interaction of these modes. This allowed one to
determine the key modes that decided post[U+2010]buckling equilibrium paths of the structure. In
the FEM numerical simulations, two algorithms were tested to solve the non[U+2010]linear problem of
stability loss: the Riks algorithm and the Newton–Raphson algorithm. The results for stable equilibrium
paths in both algorithms were identical. However, the Riks algorithm allowed us to catch the effect
of a jump between stable equilibrium paths. The detailed simulations were conducted for simple,
supported, C[U+2010]channels and angle bar with local isotropic stiffeners of the assumed lengths.
The walls of the columns under investigation were made of laminate in the elastic range. While
selecting the column lengths, the authors followed the principle that interactions between the selected
eigenmodes cause strong. The investigations of Andrzej Teter were financed within the Lublin University
of Technology – contract no. M/KMS/FD-20/M-5/122/2022. In the semi-analytical method SAM
based on Koiter’s theory, it was possible to determine the key modes that decided post[U+2010]buckling
equilibrium paths of the structure. In the FEM, it was practically impossible to choose which modes
were to be considered. Including two anti[U+2010]symmetrical modes in the perturbation method
caused a significant decrease in the load[U+2010]carrying capacity. The most crucial interactions of
anti[U+2010]symmetrical modes took place for the distortional global and local mode. The ultimate
load[U+2010]carrying capacity determined with the FEM corresponded to the SAM only if symmetrical
modes were considered. The post[U+2010]buckling equilibrium path determined with the Riks method
under low overloads was the same as that obtained with the perturbation method based on Koiter’s
theory. At higher overloads, it overestimated the ultimate load[U+2010]carrying capacity, then it
jumped onto another equilibrium path, coming closer, when only symmetrical buckling modes were
accounted for in the interaction. A jump between equilibrium paths results from the fact that new
buckling modes appear.
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