Influence of the coupling matrix B on the interactive buckling of FML-FGM columns with closed cross-sections under axial compression

The study of the coupled instabilities of thin-walled columns with trapezoidal and square cross-sections, which are made of Functionally Graded Materials (FGMs) and Fibre Metal Laminates (FMLs) is presented in the paper. It is assumed that each column wall is made of a stack of nine FML layers and/or a single FGM (Al-TiC) and/or ceramics (TiC). The GLARE 3 type FML part was made of an alternate sequence of Al 2024-T3 and even GFR prepreg layers where aluminium was always the outer layer. In the case of the FGM layer, volume fractions of ceramics and the metal distribution throughout the layer thickness are described by a simple power law. It is assumed that the columns are subjected to axial compression and simple supported at their loaded edges. All constituent materials obey Hooke's law. The effect of temperature influence is neglected. To determined governing equations of considered FML-FGM structures the classical laminate plate theory (CLPT) is used. The solution to the problem of the non-linear buckling of hybrid thin-walled structure is based on the Koiter's theory. An interaction of the global buckling mode with two local buckling modes is taken into account. In order to derive the equilibrium equations of FML-FGM profiles, the full Green's strain tensor and the second Piola-Kirchhoff's stress tensor have been adapted. The presented solution seems to be especially important as the authors have not found no earlier studies on the coupled buckling of thin-walled FML-FGM structures with closed cross-sections.