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.

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.

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.

Electric field effect on dynamic analysis of smart porosity-dependent nanocomposite sandwich plate resting on silica aerogel foundation considering carbon nanotubes agglomeration

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2651-2669
Author(s):  
Mohammad Hossein Zamani ◽  
Mohammad Heidari-Rarani ◽  
Alireza Ariaei
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Silica Aerogel ◽  
Sandwich Plate ◽  
Core Layer ◽  
Smart Structure ◽  
Geometrical Parameters ◽  
Equivalent Material ◽  
Electric Field Effect ◽  
The Core

In this study, the influence of carbon nanotubes agglomeration is investigated on the electroelastic dynamic behavior of a sandwich plate. The smart sandwich plate consists of functionally graded porous layer as the core and piezoelectric layers as the face sheets, which is subjected to the harmonic electrical loading. In order to take into account the continuum model for the silica aerogel foundation of the smart structure, the modified Vlasov’s model is applied. The porosity distribution of the core layer varies non-uniformly throughout the thickness due to the non-uniform function. The equivalent material properties of nanocomposite core layer are determined using the Eshelby–Mori–Tanaka approach, in which the influence of carbon nanotube agglomeration is considered. For modeling the electroelastic fact sheets behavior, the piezoelasticity theory is adopted. On the basis of non-polynomial shear and normal deformation theory, the governing equations of motion are inferred applying the Hamilton’s principle and the obtained equations are solved by an iterative procedure. The verification is accomplished through the available results in the literature and the influences of carbon nanotube agglomeration, different geometrical parameters, porosity index, and applied voltage are assessed on the dynamic deflection of nanocomposite sandwich plate.

scholarly journals Experimental Investigation of Stress Distributions in 3D Printed Graded Plates with a Circular Hole

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7845
Author(s):  
Quanquan Yang ◽  
He Cao ◽  
Youcheng Tang ◽  
Yun Li ◽  
Xiaogang Chen
Keyword(s):  
Experimental Investigation ◽  
Stress Concentration ◽  
Young’S Modulus ◽  
Circular Hole ◽  
Young's Modulus ◽  
Theoretical Models ◽  
Research Field ◽  
Functionally Graded ◽  
Stress Distributions ◽  
Functionally Graded Plates

An experimental investigation is presented for the stress distributions in functionally graded plates containing a circular hole. On the basis of the authors’ previously constructed theoretical model, two kinds of graded plates made of discrete rings with increasing or decreasing Young’s modulus were designed and fabricated in virtue of multi-material 3D printing. The printed graded plates had accurate size, smooth surface, and good interface. The strains of two graded plates under uniaxial tension were measured experimentally using strain gages. The stresses were calculated within the range of linear elastic from the measured strains and compared with analytical theory. It is found that the experimental results are consistent with the theoretical results, and both of them indicate that the stress concentration around the hole reduces obviously in graded plates with radially increasing Young’s modulus, in comparison with that of perforated homogenous plates. The successful experiment in the paper provides a good basis and support for the establishment of theoretical models and promotes the in-depth development of the research field of stress concentration in functionally graded plates.

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.

scholarly journals On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

2012 ◽  
Vol 19 (6) ◽  
pp. 1315-1326 ◽  
Author(s):  
Arnaldo J. Mazzei Jr.
Keyword(s):  
Young’S Modulus ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ritz Method ◽  
Turbine Blades ◽  
Functionally Graded ◽  
Graded Materials ◽  
Rotating Beams ◽  
Helicopter Blades ◽  
Aerospace Applications

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

scholarly journals On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

2012 ◽  
Vol 19 (4) ◽  
pp. 707-718 ◽  
Author(s):  
Arnaldo J. Mazzei Jr.
Keyword(s):  
Young’S Modulus ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ritz Method ◽  
Turbine Blades ◽  
Functionally Graded ◽  
Graded Materials ◽  
Rotating Beams ◽  
Helicopter Blades ◽  
Aerospace Applications

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

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