Investigation of buckling Behavior of functionally graded thin-walled box beams under axial loading

Recently, the growing needs of the engineering community for smart structures have led to targeted material technology gradually replacing conventional homogeneous and laminated composite materials. Among the sandwich-shaped structures with targeted core, the thin walled closed beam of sandwich box (with functionally graded core), due to having desirable properties such as high flexural stiffness, low density, desirable static and dynamic properties likewise high strength against mechanical loads and stresses have received much attention.
In some specific applications, components of modern structures, such as thin walled functionally graded beams with a closed box geometry, are subjected to axial or concentrated or wide transverse loads. Under these conditions, the choice of loading parameters may lead to lateral or axial buckling, which results in irrecoverable damage to the structure. Buckling of an axially loaded thin-walled functionally Graded sandwich box beam in presence of structural non-homogeneity is studied.
In this study, taking into account the effects of the structural heterogeneity (via power law distribution), porosity and effect of the cross-sections warping by means of Vlasov’s beam assumptions and applying the Hamilton’s principal the governing equations of the Buckling instability of the thin-walled functionally graded sandwich box porous beam were derived. Then the finite element method was developed to formulate the problem. In following, for the case of various boundary conditions, the related governing eigenvalue problem was derived and solved numerically. The validity of the results was accomplished by comparing the results with those of the literature. In following beside by providing the characteristic buckling curves, the effect of different parameters of the problem, including the beam aspect ratio, mixing volume fraction index, porosity index, core component modulus ratio and ceramic layer thickness on the buckling load were investigated comprehensively. It was observed that different parameters, especially the mixing index and structural porosity index has a considerable influence in determining the buckling boundary.