Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations

Abstract

In this article, an analytical study was done to predict the behavior of the beam vis-à-vis bending, buckling, and dynamic responses of isotropic homogeneous beams based on an elastic foundation. The material properties of the FG-beams vary across the thickness using the power law. In this work, the sinusoidal shear deformation beams theory is used to investigate the static and dynamic behavior of FG beams. The present theory fulfills the condition of nullity of edge stresses and does not require the use of a shear correction factor. Hamilton's principle is used to deduce equations of motion, and analytical solutions for simply supported beams were obtained using the Navier resolution method. Nondimensional displacements, eigenfrequencies and critical-buckling loads of isotropic homogeneous beams were obtained for various values of the foundation parameters. The numerical results obtained by the present technique have been compared with the results of literature and are in excellent agreement with them. It can be concluded that the current HSDBT is simple and accurate in solving the bending, eigenfrequency and critical-buckling load problems for FGM beams.

A novel high order theory for static bending of functionally graded (FG) beams subjected to various mechanical loads

“…Pei-Liang B et al [12] employed a new FEM framework to analyze the mechanical responses of nanobeams made of axially functionally-graded material (FGM) under different boundary conditions. Chitour et al [13] introduced a novel hyperbolic quasi-3D shear deformation plate theory for analyzing the bending behavior of functionally graded sandwich plate structures submitted to sinusoidal loads, while Chikh et al [14] investigated the static response and free vibration of a functionally graded beam on elastic foundations. Thai et al [15] explored the free vibration and bending of FG beams using higher-order beam theories, and a refined plate theory was developed for examining thermoelastic effects and wave propagation in functionally graded plates.…”

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

“…Reddy et al [1][2][3] used thirdorder shear deformation theory to study the mechanical behavior of isotropic and FG plates and beams. Following that, several research projects have been carried out in order to develop new theories based on Reddy's theory (e.g., hyperbolictrigonometric [4][5][6][7][8][9][10][11][12][13], trigonometric [14][15][16][17][18], exponential [19], trigonometric-exponential [20], exponential-logarithmic [21], and polynomial [22][23][24][25]). Li et al [26][27][28] studied static and free vibration behavior of FG plates employing novel polynomial theories with shape parameter (m).…”