Investigation on the Analysis of Bending and Buckling for FGM Euler-Bernoulli Beam Resting on Winkler-Pasternak Elastic Foundation

Abstract

Abstract In this paper, Functionally Graded Material (FGM) has been analyzed to examine bending and buckling of simply supported beams. Using Euler-Bernoulli beam theory (EBT), these beams that rested on Winkler-Pasternak elastic foundation are exposed to two types of loads that are axial compressive force and distributed transverse load. Here, based on power-law distributions, the properties of the material of FGM beam is assumed to be varied at the direction of the thickness. The derivation of the FGM beams’ governing equations was done using the total potential energy principle. The transverse deflection and the critical buckling of the FGM beam were determined using the Navier-type solution method with simple boundary conditions. A closure on the effects of the power-law exponent of FGM, and the spring constant with the shear constant of elastic foundation on the transverse deflection and critical buckling load was achieved. A validation study for numerical results was carried out here with previous results from the literature and they are said to be in excellent agreement. It is shown by the numerical results that critical buckling load is decreasing with increasing both, slenderness ratio and values of power-law exponent and vice versa for transverse deflection.