Static interactive buckling of functionally graded columns with closed cross-sections subjected to axial compression

The present paper deals with static coupled buckling of thin-walled columns with trapezoidal and square cross-sections, which are made of functionally graded materials (FGMs). An Al-TiC, metal-ceramic material is applied. The discussion assumed that the columns were axial compressed and simple supported at their ends. In addition, the material is subject to Hooke's law. The effect of temperature is neglected. The classical laminate plate theory (CLPT) has been used to describe properties of the functionally graded structures. The problem of the non-linear buckling was solved by using a variational method for the asymptotic analytical-numerical method (Koiter's theory). Static interaction of the global buckling mode with the two local buckling modes has been taken into account. In order to derive the equilibrium equations of functionally graded structures, the full Green's strain tensor and the second Piola-Kirchhoff's stress tensor has been adapted. The presented problem is particularly important as the authors have found no earlier studies on coupled buckling of thin-walled functionally graded structures with closed cross-sections.