Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Inversion of Functionally Graded Materials to Improve the Elastic Ultimate Bearing Capacity of Thick-Walled Hollow Cylinder

2011 ◽  
Vol 378-379 ◽  
pp. 116-120 ◽  
Author(s):  
Ai Zhong Lu ◽  
Ning Zhang
Keyword(s):  
Bearing Capacity ◽  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ultimate Bearing Capacity ◽  
Functionally Graded ◽  
The Body ◽  
Graded Materials ◽  
Homogeneous Materials

Thick-walled hollow cylinder is an important class of engineering structure, the stress state of which depends on the loads and properties of the body materials. Under the assumptions of σθ-σr=c (σθ and σr denote the hoop stress and radial stress, respectively, c is a constant), inverse analysis of thick-walled hollow cylinder composed of functionally graded materials with uniform pressure acting on the outer surface is carried out. Analytical solutions for the Young’s modulus variation in the radial direction are obtained. It is found that only when the Young’s modulus E(r) is a specific monotone increasing function of the radius r, the pre-specified stress distribution can be satisfied. Comparing with classical homogeneous materials, stress concentration at the inner surface of hollow cylinder composed of functionally graded materials can be alleviated. Hence the elastic ultimate bearing capacity of hollow cylinder can be improved strikingly. For functionally graded materials, the elastic ultimate bearing capacity can be improved strikingly by increasing the thickness of cylinder, which is not so obvious for classical homogeneous materials.

Perforated Functionally Graded Plate with Arbitrarily Radial Variation of Young’s Modulus under Pure Shear

2011 ◽  
Vol 337 ◽  
pp. 678-681
Author(s):  
Hao Li ◽  
Yi Hua Liu
Keyword(s):  
Young’S Modulus ◽  
Function Method ◽  
Series Solution ◽  
Radial Direction ◽  
Young's Modulus ◽  
Pure Shear ◽  
Functionally Graded ◽  
Static Response ◽  
Functionally Graded Plate ◽  
Stress Function Method

In this work, the static response of a perforated functionally graded plate is investigated under pure shear. Young’s modulus is assumed to vary arbitrarily along the radial direction, while Poisson’s ratio keeps constant. Using the stress function method, the governing equation is obtained, and then the series solution of stresses is derived with the aid of the Frobenius method. Numerical examples show that the convergence rate of the presented solution is rapid.

Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

2009 ◽  
Vol 44 (4) ◽  
pp. 249-261 ◽  
Author(s):  
Y P Xu ◽  
D Zhou
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Lower Surface ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Line ◽  
Simply Supported ◽  
Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

Manufacturing and Measuring Mechanical Properties of Continuous Functionally Graded Beam

2021 ◽  
Vol 21 (2) ◽  
pp. 7-11
Author(s):  
Ahmed Mansoor Abbood ◽  
Haider K. Mehbes ◽  
Abdulkareem. F. Hasan
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
High Concentration ◽  
Functionally Graded Beam ◽  
Low Concentration ◽  
Graded Material ◽  
Vertical Gravity

In this study, glass-filled epoxy functionally graded material (FGM) was prepared by adopting the hand lay-up method. The vertical gravity casting was used to produce a continuous variation in elastic properties. A 30 % volume fraction of glass ingredients that have mean diameter 90 μm was spread in epoxy resin (ρ = 1050 kg/m3). The mechanical properties of FGM were evaluated according to ASTM D638. Experimental results showed that a gradually relationship between Young’s modulus and volume fraction of glass particles, where the value of Young’s modulus at high concentration of glass particles was greater than that at low concentration, while the value of Poisson’s ratio at high concentration of glass particles was lower than that at low concentration. The manufacture of this FG beam is particularly important and useful in order to benefit from it in the field of various fracture tests under dynamic or cyclic loads.

Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation

2017 ◽  
Vol 21 (8) ◽  
pp. 2700-2734 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
MH Zamani
Keyword(s):  
Young’S Modulus ◽  
Silica Aerogel ◽  
Young's Modulus ◽  
Nonlocal Parameter ◽  
Core Layer ◽  
Functionally Graded ◽  
Electric Field Effect ◽  
Governing Equations ◽  
Model Foundation ◽  
Mechanical Bending

In the present research electro-mechanical bending behavior of sandwich nanoplate with functionally graded porous core and piezoelectric face sheets is carried out. Vlasov’s model foundation is utilized to model the silica Aerogel foundation. Two functions are considered for nonuniform variation of material properties of the core layer along the thickness direction such as Young’s modulus, shear modulus, and density. The governing equations are deduced from Hamilton’s principle based on sinusoidal shear and normal deformation theory. In order to solve seven governing equations, an iterative technique is accomplished. After all, deflection and stresses are verified with corresponding literatures. Eventually, the numerical results reveal that applied voltage, plate aspect ratio, thickness ratio, nonlocal parameter, porosity index, Young’s modulus, and height of silica Aerogel foundation have substantial effects on the electro-mechanical bending response of functionally graded porous sandwich nanoplate.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk With Nonuniform Thickness and Variable Angular Velocity

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Y. Zheng ◽  
H. Bahaloo ◽  
D. Mousanezhad ◽  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Radial Direction ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Outer Radius ◽  
Functionally Graded ◽  
Circumferential Direction ◽  
Stress Fields ◽  
Fiber Reinforced ◽  
Inner Radius ◽  
Nonuniform Thickness

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

Analytical Solution and Experimental Study of Effective Young's Modulus of Selective Laser Melting-Fabricated Lattice Structure With Triangular Unit Cells

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Jie Niu ◽  
Hui Leng Choo ◽  
Wei Sun ◽  
Sui Him Mok
Keyword(s):  
Analytical Solution ◽  
Young’S Modulus ◽  
Selective Laser Melting ◽  
Triangular Lattice ◽  
Young's Modulus ◽  
Numerical Results ◽  
Lattice Structures ◽  
Shape Parameters ◽  
Laser Melting ◽  
Unit Cells

Research on materials, design, processing, and manufacturability of parts produced by additive manufacturing (AM) has been investigated significantly in the past. However, limited research on tensile behavior of cellular lattice structures by AM was carried out. In this paper, effective tensile Young's modulus, E*, of triangular lattice structures was determined. Firstly, analytical solution was derived based on Euler–Bernoulli beam theory. Then, numerical results of E* were obtained by finite element analysis (FEA) for triangular lattice structures classified by three shape parameters. The effects of side length, L, beam thickness, t, and height, h, on E* were investigated individually. FEA results revealed that there is a relationship between E* and the relative density and shape parameters. Among them, t has the most significant effect on E*. Numerical results were also compared with the results from modified general function for cellular structures and modified formula for triangular honeycomb. The E* predicted by the proposed analytical solution shows the best agreement with the numerical results. Finally, tensile tests were carried out using AlSi10 Mg triangular lattice structures manufactured by selective laser melting (SLM) process. The experimental results show that both analytical and numerical solutions are able to predict E* with good accuracy. In the future, the proposed solution can be used to design lightweight structures with triangular unit cells.

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