Bending and buckling of a metal seven-layer beam with crosswise corrugated main core – Comparative analysis with sandwich beam

Abstract

The study is devoted to thin-walled simply supported sandwich beams: three and seven-layer beams. Seven-layer beams are composed of a trapezoidally crosswise corrugated main core and two three-layer facings with trapezoidally lengthwise corrugated cores. Essential difference between such a structure and classical three-layer beams consists in the fact that the facings are of three-layer structure too. Hence, the structure is a seven-layer beam, the layers of which are distinguished by different properties. The thin-walled beam with three trapezoidally corrugated cores is an innovatory orthotropic structure, not referred to in the literature. Characteristic feature of the beam consists in differentiation of shear effects in particular layers, according to the core corrugation direction. Deformation of the cross section of the beam depends on the direction too. An original mathematical model is formulated, which includes the hypothesis of deformation of the cross section of the beam, inclusive of the displacement and strain fields, and rigidities of the layers in particular directions. The adequate model of three-layer beam with steel foam core is also formulated. Basing on the principle of the total potential energy the equations of equilibrium are derived for three and seven-layer beams, respectively. Then the equations are analytically solved. In case of seven-layer beams the deflections and the critical axial force are determined for different values of the trapezoidal corrugation pitch of the main core. The results are compared with adequate for three-layer beam and presented in Tables. It is concluded that such seven-layer beam – plate band with three-layered facings is more resistant to the load than the classical three-layered beams of the same mass with regard to strength and stability. Additional effect of the research consists in generalization of classical theories of sandwich plates.