Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory

A new refined quasi-3D shear deformation theory for bending, buckling, and free vibration analyses of a functionally graded porous beam resting on an elastic foundation is presented. It involves only three unknown functions, against four or more ones in other shear and normal deformation theories. The stretching effect is naturally taken into account by this theory because of its 3D nature. The mechanical characteristics of the beam are assumed to be graded in the thickness direction according to two different porosity distributions. The differential equation system governing the bending, buckling, and free vibration behavior of porous beams is derived based on the Hamilton principle. The problem is then solved using the Navier solution for a simply supported beam. The accuracy of the present solution is demonstrated by comparing it with other closed-form solutions available in the literature. A detailed parametric study is presented to show the influence of porosity distribution on the general behavior of FG porous beams on an elastic foundation.