The static and free vibration analyses of axially functionally graded elliptical beams via mixed FEM

Abstract

The objective of this study is to investigate the behavior of the static and free vibration analyses of axially functionally graded elliptical planar curved beams using a mixed finite element method (MFEM) based on the Timoshenko beam theory. A two-noded curved mixed finite element has 12 field variables at each node. These variables denote three displacements, three cross-sectional rotations, three forces, two bending moments, and torque, respectively. The functionally graded material is composed of ceramic-particle material and metal-matrix material. The volume fraction of ceramic and metal materials varies along the beam axis. The effective material properties (modulus of elasticity, Poisson's ratio, and density) of the functionally graded material are determined according to the rule of mixture. It is aimed in the benchmark examples to present the influence of ceramic-particle material and non-homogeneity index of material gradation, the minimum radius of the elliptical beam, and boundary condition to the results of static and free vibration analysis in detail.

An investigation on the torsional vibration of a FG strain gradient nanotube

“…Static analysis of FG beams with porous form has been presented by Ermiş et al. [28] with the mixed finite element method. Nejadi et al.…”

“…Ermiş et al. [69] have presented the static and vibration analyses of elliptical beams with material properties varying in the axial direction using the mixed finite element method. The two phase local/nonlocal deformation of thermo electrical reinforced composites was studied by Selvamani et al.…”

“…[70] with the Navier method. It is possible to see these methods used in the briefly mentioned articles and in other studies [28, 29, 49, 53, 71–77] as well. In our study, Fourier sine series with Stokes’ transform is considered for functionally graded porous nanotubes.…”

“…Ramteke et al [25][26][27] have studied the mechanical responses of 2D functionally graded panel structures with porosity effects. Static analysis of FG beams with porous form has been presented by Ermiş et al [28] with the mixed finite element method. Nejadi et al [29] have investigated the stability and dynamic of reinforced sandwich pipe based on effect of porosity.…”

“…Bian and Qing [68] have demonstrated the vibration and stability of nonlocal strain gradient thin beams with Laplace transform. Ermiş et al [69] have presented the static and vibration analyses of elliptical beams with material properties varying in the axial direction using the mixed finite element method. The two phase local/nonlocal deformation of thermo electrical reinforced composites was studied by Selvamani et al [70] with the Navier method.…”