scholarly journals A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

2021 ◽  
Vol 11 (24) ◽  
pp. 11747
Author(s):  
Fadi Althoey ◽  
Elias Ali
Keyword(s):  
Shear Stress ◽  
Stress Analysis ◽  
Elastic Moduli ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Material Function ◽  
Functionally Graded Beam ◽  
Structural Applications ◽  
Beam Thickness ◽  
Fgm Beam

This paper aims at providing a simplified analytical solution for functionally graded beam stress analysis and optimized material gradation on the beam deflection. The power-law (P-FGM) and exponential (E-FGM) material functions were considered for an exact solution of the normal and shear stress distributions across the beam thickness. Optimization of material function on the FGM beam deflection, which is new of its kind, was also investigated considering both simply supported and cantilever beams. It was observed that the non-dimensional normal stress and shear stress are independent of the elastic moduli values of the constituent materials but rather depends on both the ratio of the elastic moduli and the location across the beam thickness in the E-FGM material function model. This observation was first validated from available kinds of literature and through numerical simulation using ABAQUS and extended to the P-FGM stress analysis. The maximum deflection on the FGM beam occurred for a homogenous steel beam while the minimum deflection was observed on the beam with a P-FGM material function. The results of this work demonstrate that if properly designed and optimized, FGMs can provide an alternative material solution in structural applications.

scholarly journals ON THE MECHANICAL RESPONSE OF A PRESSURIZED FUNCTIONALLY-GRADED CYLINDER

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Vlado Lubarda
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Functionally Graded Material ◽  
Elastic Moduli ◽  
Mechanical Response ◽  
Maximum Shear Stress ◽  
Radial Distance ◽  
Functionally Graded ◽  
Graded Material ◽  
Radial Inhomogeneity

A pressurized functionally-graded cylinder is considered made of the material whose elastic moduli vary with the radial distance according to the power-law relation. Some peculiar features of the mechanical response are noted for an incompressible functionally-graded material with the power of radial inhomogeneity equal to two. In particular, it is shown that the maximum shear stress is constant throughout the cylinder, while the displacement changes proportional to 1/r along the radial distance. No displacement takes place at all under equal pressures applied at both boundaries.

scholarly journals Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

2017 ◽  
Vol 39 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc ◽  
Nguyen Tien Khiem
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Functionally Graded Beam ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Fgm Beam

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

Coupled Thermo-Mechanical Transient Stress Analysis of Functionally Graded Gas Turbine Rotor

2015 ◽  
Author(s):  
Dinesh Patil ◽  
D. Koteswara Rao ◽  
Tarapada Roy
Keyword(s):  
Shear Stress ◽  
Stress Analysis ◽  
Gas Turbine ◽  
Power Law ◽  
Shear Deformation Theory ◽  
Axial Direction ◽  
Turbine Rotor ◽  
Functionally Graded ◽  
Graded Materials ◽  
Turbine Shaft

This paper is concerned with the coupled thermo-mechanical stress analysis of functionally graded (FG) gas turbine rotor shaft system. Gas turbine shaft may expose in high temperature environments which demands to use functionally graded materials (FGMs). The aim of the present work is to study the stresses developed in the FG turbine shaft due to temperature variations and mechanical loading due to unbalance masses. For the present analysis aluminum oxide (Al2O3) and stainless steel (SUS304) are taken as shaft materials, power law gradation is used for the determination of FG material properties of the turbine shaft. Three nodded Timoshenko beam element with six degree of freedom (DOF) per node is considered for the finite element modelling of FG shaft. First order shear deformation theory (FSDT) is used with rotary inertia, strain and kinetic energy. Solution for governing equation of motion is obtained by the Hamilton principle. Complete MATLAB code has been developed for thermosmechanical stress analysis. Comparative study between steel shaft and FG shaft have been carried out. Normal stress (σxx) on plane perpendicular to axial direction, shear stress (τxr) on plane perpendicular to axial direction in radial direction and shear stress (τxθ) on plane perpendicular to axial direction in circumferential direction are obtained against time and along radius of shaft. Also these stresses are obtained for different parameters like power law indexes and speed of rotation of shaft.

Comparison of Post-Buckling Behaviors of a S-S FGM Beam under Conservative and Non-Conservative Distributed Forces

2011 ◽  
Vol 250-253 ◽  
pp. 266-270
Author(s):  
Qing Lu Li ◽  
Shi Rong Li
Keyword(s):  
Deformation Theory ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Conservative System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Beam ◽  
Post Buckling ◽  
Fgm Beam ◽  
Distributed Forces

Based on the large deformation theory and considering the axial extension of the beam, the governing equations of post-buckling of a simply supported elastic FGM beam subjected to conservative and non-conservative distributed forces were established. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using shooting method, the nonlinear boundary-value problem was solved numerically and the equilibrium paths as well as the post- buckling configurations of the deformed beam were presented. A comparison between the results of conservative system and that of non-conservative systems were given. The results shows that the features of the equilibrium paths of the the functionally graded beam under non-conservative are evidently different from those to a conservative one.

Analytical responses of functionally graded beam under moving mass using Caputo and Caputo–Fabrizio fractional derivative models

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1859-1867 ◽  
Author(s):  
Ibrahim M Abu-Alshaikh ◽  
Amro A Almbaidin
Keyword(s):  
Fractional Derivative ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Moving Mass ◽  
Functionally Graded Beam ◽  
The Laplace Transform ◽  
Voigt Model ◽  
The Difference ◽  
Euler Bernoulli Beam

In this article, a functionally graded simply supported Euler–Bernoulli beam subjected to moving mass is considered in which the beam-damping is described using fractional Kelvin–Voigt model. A comparison between Caputo and Caputo–Fabrizio fractional derivatives for obtaining the analytical dynamic response of the beam is carried out. The equation of motion is solved by the decomposition method with the cooperation of the Laplace transform. Two verification studies were performed to check the validity of the solutions. The results show that the grading order, the velocity of the moving mass and the fractional derivative order have significant effects on the beam deflection, whereas the difference between the results of the two fractional derivative models is expressed by the determination of the correlation coefficient.

scholarly journals Vibrations piezo-control of FGM beam in a thermal environment

2019 ◽  
Vol 286 ◽  
pp. 01001
Author(s):  
K. El Harti ◽  
MED. Rahmoune ◽  
M. Sanbi ◽  
R. Saadani ◽  
M. Bentaleb ◽  
...  
Keyword(s):  
Thermal Environment ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Functionally Graded ◽  
Flexible Beam ◽  
Sensors And Actuators ◽  
Functionally Graded Beam ◽  
Piezoelectric Sensors And Actuators ◽  
Active Vibration ◽  
Fgm Beam

An analytical method on the active vibration control of a functionally graded beam equipped with layers of piezoelectric sensors and actuators, in a thermal environment, is studied. The study based on Euler-Bernoulli theory and finite element method, applied to a flexible beam divided into a finite number of elements. The equations of motion are obtained by applying the principle of Hamilton. The structure is modeled analytically then numerically and the results of the simulations are presented to visualize the states of their dynamics.

Free Vibration Analysis the Cracked FGM Beam under Bending-Torsion Loading, Using GDQ Method

2013 ◽  
Vol 330 ◽  
pp. 942-947 ◽  
Author(s):  
Alireza Daneshmehr ◽  
D.J. Inman ◽  
A. Mohammadi Fakhar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Functionally Graded Beam ◽  
Fg Beam ◽  
Fgm Beam

This paper presents a theoretical investigation of free vibration analysis of a functionally graded beam (FGM) under the bending-torsion loading using a classical elasticity theory. The FG beam is assumed to have an open edge crack. It is assumed that the material properties of the simply-supported cracked beam, vary along the beam thickness following a polynomial distribution in the thickness direction. This analysis is based on the linear fracture mechanics. First of all, governing equations and boundary conditions of the FG beam are derived using Hamilton's principle. The governing equations are solved using generalized differential quadrature (GDQ) method. By applying GDQ method, the governing differential equations convert to a linear system of algebraic equations. Then solving the eigenvalue problem, natural frequencies of the FG beam can be found. The results indicate that natural frequencies in the presence of a crack are affected by the crack ratio and location.

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