Bending and Free Vibration Analysis of Functionally Graded Sandwich Pile on Elastic Foundation Using Rayleigh-Ritz Method

The present study aims to carry out a parametric investigation on a pile made of different materials, and subjected to static and dynamic loading resulting from the weight of the structure and the shear force acting on the head of the pile. It is worth specifying that the pile is anchored in the ground on a Winkler-Pasternak elastic foundation that is made up of five different layers. In this study, the equilibrium equations were treated using the high-order theory with a new shear deformation shape function of a cylindrical pile made of an isotropic material and a sandwich functionally graded material.The results obtained with a numerical study based on the minimization of energies by the Rayleigh-Ritz method was carried out in order to highlight the influence of the geometric ratio, the volume fraction of the functionally graded material, and the type of loading on the vibration frequencies and the admissible stresses in order to determine the most appropriate material for the pile so that extreme stresses can be absorbed. The precision and the applicability of the method with new solution of the transverse shear deformation are demonstrated through this study with modeling of the layered property of the soil, were then compared with those reported in previous work available in the literature. It turned out that these results are in good agreement with each other, for the different materials of pile and for all boundary conditions considered. The results of pile with sandwich functionally graded material, it is revealed that the role of this material has an influence on the type of loading, especially, in the case statique of a pile subjected to a compound bending weight and the shear effect, in case dynamique the pile with vibration flexible or rigid .