Effect of Phase Contrast and Geometrical Parameters on Bending Behavior of Sandwich Beams with FG Isotropic Face Sheets

Abstract

Our work is to study the bending behavior of sandwich beams with functional gradient by constituting an isotropic material whose material properties vary smoothly in the z direction only (FGM), where the central layer presents purely a homogeneous and isotropic ceramic. The mechanical properties of FG sandwich beams are assumed to be progressive in thickness according to a power law (P-FGM). Generally, the principle of virtual works is used to obtain the equilibrium equations, and their solutions are obtained based on Navier's solution technique. The present model is based on a shear deformation theory of 2D and 3D beams which contains four unknowns to extract the equilibrium equations of FG sandwich beams. In addition, analytical solutions for bending are used and numerical models are presented to verify the accuracy of the present theory. All the results obtained show that the stiffness of the FG beam decreases as a function of the increase in the volume fraction index k, leading to an increase in the deflections. However, FG beams become flexible by increasing the proportion of the metal to the ceramic part. Furthermore, the influences of material volume fraction index, layer thickness ratio, side-to-height ratio, and the effect of the phase contrast, on the deflections, normal and shear stress of simply supported sandwich FG beams are taken into investigation and discussed in detail. Finally, all our results obtained are in agreement with other previous theoretical works.