Keywords: sandwich structure, deflection, metal foam, mathematical modelling, five layer beam, numerical model.

The subject of this paper is the analysis of the deflection of a five layer sandwich beam. The mechanical and physical properties vary through the thickness of the beam and depend on the material of each layer. The two faces of the beam are thin aluminium sheets and the core is made of aluminium foam. Between the faces and the core there are two thin binding glue layers. The beam is considered then as a five layer sandwich beam. The main goal of the paper is to present a mathematical model of the five layer beam and to compare the results of the analyses obtained analytically and numerically.

A simply supported sandwich beam of the length and the width carries a concentrated force. The force is located in the middle of the beam. For this load, a mathematical model of the field of displacements, which include a shared effect and a bending moment, is presented. The system of partial differential equations for the equilibrium of the five layer sandwich beam is derived on the basis of the principle of stationary total potential energy. From three equations, after transformations, two equations are obtained. These equations are approximately solved by means of the Bubnov-Galerkin method. After simply transformations the deflection is obtained. The influence of the binding layer thickness and Young's modulus on the value of the deflection is compared.

For comparison a finite element model of the beam is formulated. The model is composed of four-node shell elements for the faces and eight-node brick elements for the core. The binding layers are modelled by proper tie constraints between the layers. The deflection analysis has been performed on the family of sandwich beams, in which the load has been determined. Comparison of the results obtained in the analytical and numerical (MES) analysis are shown in graphs and figures. A poor agreement can be seen between this two analysis (20%). Probably this is because of too large an approximation of the orthogonal functions. An increase in the degrees of freedom for these functions should reduce the difference to a few percent.

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