Static deflection analysis of functionally graded beams using various beam theories

Abstract

In the current study, static deflection analysis of a functionally graded (FG) beam is carried out for various theories such as Euler, Timoshenko, and high-order shear deformation theory. The governing equation was solved using the minimum total potential energy principle. Further, for different types of loads, the static deflection analysis of the FG beam was performed using Navier’s solution using the Fortran programming language. Moreover, finite element analysis was also carried out using ANSYS software. In this method, each layer of the FG beam possesses different material properties as per a power law distribution. The different solution techniques are used to calculate the static deflection, and their results are compared. Effect of various parameters such as power index value, modulus ratio, aspect ratio (L/h), and type of loading on the dimensionless transverse deflection of this FG beam model. The results show that the aspect ratio has no significant effect on transverse dimensionless deflection in the case of the Euler beam theory. However, there is a noticeable effect for the Timoshenko and higher-order shear deformation theories, indicating that shear significantly impacts dimensionless transverse deflection for short beams. In addition, it is proven that the present model is reliable and can calculate the static deflection for any other required beam with different loads and dimensions.