Buckling Analysis of Rectangular Beams Having Ceramic Liners at Its Top and Bottom Surfaces with the help of the Exact Transfer Matrix

In this study the elastic buckling behavior of beams with rectangular cross section is studied analytically. It is assumed that both the top and bottom surfaces of the beam are ceramic coated. The aluminum (Al) is chosen as a core material while the aluminum-oxide (Al2O3) is preferred as a liner (face) material. The transfer matrix method based on the Euler-Bernoulli beam theory is employed in the analysis. The exact transfer matrix in terms of equivalent bending stiffness is presented together with the exact buckling equations for hinged-hinged, clamped-hinged, clamped-free, and finally clamped-clamped boundary conditions. After verifying the results for beams without liners, dimensionless buckling loads of the beam with ceramic liners are numerically computed for each boundary condition. The effect of the thickness of the ceramic liner on the buckling loads is also investigated. It is found that a ceramic liner enhances noticeably the buckling loads. As an additional study those effects are also examined for the ratios of elasticity modulus of face material to core material in a wide range.