Effective design of a sandwich beam with a metal foam core

The subject of the paper is a simply supported sandwich beam with a metal foam core. Mechanical properties of the core vary through its depth. A nonlinear hypothesis of deformation of a plane cross section of the beam is assumed and described. The elastic potential energy and the work of the load are formulated. The system of differential equations of the equilibrium is derived on the basis of the theorem of minimum total potential energy. The system of equations is analytically solved. The stress state and the critical force for the beam are determined. The optimal dimensionless parameters of the beam are calculated. Results of the numerical investigations are presented in figures.