Unsymmetrical sandwich beams under three-point bending - Analytical studies

The main purpose of the work is an analytical description of a simply supported three-layer beam with facings of various thicknesses and various material constants. The beam core is made of metal foam. Its mechanical properties are described. The beam is subjected to three-point bending. The analytical model of the beam is formulated based on a nonlinear hypothesis of deformation of the cross section of the beam. The proposed hypothesis is a generalization of the classical one - the broken line hypothesis. The linear relationship between the strains and displacements is assumed. Stresses are defined according to the Hooke's law. Furthermore, the elastic strain energy and the work of the load is defined. Based on the principle of the total potential energy the system of equilibrium equations is derived. Afterwards, the system is analytically solved with the use of trigonometric series. The maximum deflections and shear stresses are obtained. Moreover, the position of the neutral axis is determined. The calculations for the family of beams are carried out. The results are compared to FEM (Finite Element Method) solutions obtained from SolidWorks Simulation system.