Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy

2000 ◽  
Vol 35 (1) ◽  
pp. 13-20 ◽  
Author(s):  
W Q Chen
Keyword(s):  
Stress Distribution ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Functionally Graded ◽  
Spherical Isotropy ◽  
Graded Material

Finite Element Analysis of Human Tibia Modeled as a Functionally Graded Material

2019 ◽  
Vol 2 (3) ◽  
Author(s):  
Ashish Tiwari ◽  
Pankaj Wahi ◽  
Niraj Sinha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Distribution ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Functionally Graded ◽  
Element Analysis ◽  
Cross Sectional ◽  
Human Tibia ◽  
Graded Material

Human tibia, the second largest bone in human body, is made of complex biological material having inhomogeneity and anisotropy in such a manner that makes it a functionally graded material. While analyses of human tibia assuming it to be made of different material regions have been attempted in past, functionally graded nature of the bone in the mechanical analysis has not been considered. This study highlights the importance of functional grading of material properties in capturing the correct stress distribution from the finite element analysis (FEA) of human tibia under static loading. Isotropic and orthotropic material properties of different regions of human tibia have been graded functionally in three different manners and assigned to the tibia model. The nonfunctionally graded and functionally graded models of tibia have been compared with each other. It was observed that the model in which functional grading was not performed, uneven distribution and unrealistic spikes of stresses occurred at the interfaces of different material regions. On the contrary, the models with functional grading were free from this potential artifact. Hence, our analysis suggests that functional grading is essential for predicting the actual distribution of stresses in the entire bone, which is important for biomechanical analysis. We find that orthotropic nature of the bone tends to increase the maximum von Mises stress in the entire tibia, while inclusion of cross-sectional inhomogeneity typically increases the stresses across normal cross section. Accordingly, our analysis suggests that both orthotropy as well as cross-sectional inhomogeneity should be included to correctly capture the stress distribution in the bone.

Analytical Solution for the Thermopiezoelastic Behavior of a Smart Functionally Graded Material Hollow Sphere Under Radially Symmetric Loadings

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
M. Jabbari ◽  
A. R. Barati
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Material Properties ◽  
Functionally Graded ◽  
Feedback Gain ◽  
Modern Engineering ◽  
Graded Material ◽  
Power Law Function ◽  
Fgm Layer

An analytical study of the piezothermoelastic behavior of a functionally graded material (FGM) hollow sphere with integrated piezoelectric layers as a sensor and actuator under the effect of radially symmetric thermo-electro-mechanical loading is carried out. The material properties of the FGM layer are assumed to be graded in the radial direction according to a power law function. Governing differential equations are developed in terms of the components of the displacement field, the electric potential and the temperature of each layer of the smart FGM hollow sphere. The resulting differential equations are solved analytically. Numerical examples are given and discussed to show the significant influence of grading index of material properties and feedback gain on the mechanical–electrical responses. This will be useful for modern engineering design.

Elastoplastic Analysis of a Functionally Graded Material Beam Subjected to Uniformly Distributed Load

2019 ◽  
Vol 36 (1) ◽  
pp. 73-85
Author(s):  
L. J. Xue ◽  
X. Y. Bian ◽  
J. J. Feng ◽  
J. N. Liu
Keyword(s):  
Stress Distribution ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Average Stress ◽  
Elastoplastic Material ◽  
Elastoplastic Behavior ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Graded Material ◽  
Fgm Beam

ABSTRACTThe elastoplastic behavior of a Functionally Graded Material (FGM) simply supported beam consisting of elastic material A and elastoplastic material B under uniformly distributed load is investigated. A power function is used to describe the volume fractions of the constituent materials, and the average stress of the FGM beam is obtained by using the averaging method. This method can avoid the assumption of the varying properties of the whole material, and can consider the different Possion’s ratios of the different constituent materials. What’s more, only the elastoplastic material B in the FGM beam will yield, and the yield function is determined by the stress of material B only, rather than the average stress of the whole material. The method used in this work is more closer to the real material than the method by assuming the variation of the whole properties of FGM. The theoretical results show a good agreement with the finite element results, which indicates that the method provided in this work is valid. With this method, the variation of the elastic and plastic areas, the stress distribution on the cross section, variation of the curvature and neutral layer, and the residual stress distribution of the FGM beam are discussed through numerical results. This work can provide a new way for the design and in-depth investigation of FGM material.

Solution for Equation of Two-Dimensional Transient Heat Conduction in Functionally Graded Material Hollow Sphere With Piezoelectric Internal and External Layers

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Power Functions ◽  
Legendre Series ◽  
Graded Material

In this paper, an exact solution for the equation of two-dimensional transient heat conduction in a hollow sphere made of functionally graded material (FGM) and piezoelectric layers is developed. Transient temperature distribution, as a function of radial and circumferential directions and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and Legendre series. The results are the sum of transient and steady-state solutions that depend upon the initial condition for temperature and heat source, respectively. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r.

Sign in / Sign up

Export Citation Format

Share Document