Rkl Um 2010 Curriculum Vitae

8/3/2019 Rkl Um 2010 Curriculum Vitae

1/25

CURRICULUM VITAE

PERSONAL DETAIL

Name Dr. Ramesh Kumar Lalwani

Designation Senior Research Fellow

Department Department of MechanicalEngineering

Faculty Faculty of Engineering

Tel. No. (Office) 60379676815

Fax No. +60379675317

E-mail Address [email protected]

Homepage URL

mechanical.eng.um.edu.my/ramesh...

ResearcherID Link C-8659-2009 112508...

Address(Office) Department of MechanicalEngineering, Faculty of EngineeringUniversity of Malaya, 50603 KualaLumpur, MALAYSIA

ACADEMIC QUALIFICATION(Qualification), (Institution).

Ph.D. (Mechanical Engineering)(IIT Kharagpur), INDIAN INSTITUTE OF TECHNICAL,KHARAGPUR

M. tech, INDIAN INSTITUTE OF TECHNICAL, KHARAGPUR

B. Sc. [Engineering], VIKRAM UNIVERSITY, UJJAIN, INDIA

PROFESSIONAL AFFILIATION/MEMBERSHIP(Organisation), (Role), (Year), (Level).

NFPA, Member, 2000, (National)

INSTITUTE OF ENGINEERIS [INDIA], Honorary Fellow, 1995, (National)

THE INDIAN SOCIETY FOR TECHNICAL EDUCATION, Life Member, 1993,(National)

CAREER HISTORY(Post), (Organisation), (Period).

Adiministration, Teaching, Research And Consultancy, SKYLINE INSTITUTE OF


2/25

ENGINEERING AND TECHNOLOGY, 22/05/2008 until 05/06/2009

AREAS OF EXPERTISE(Area).

Noise And Vibrations (Design, Noise and Vibrations)

Acoustic Engineering (Noise, vibrations, dynamic stress analysis, )

RECENT SELECTED PUBLICATIONS(Publication).

Academic Journals

2010

reza afshar; M. Bayat, Dr.; R. K Lalwani, Prof.; Y.H. Yau, Associate Prof. (ISI-CitedPublication)

2009

Proceeding IUTAM Symposium on Emerging Trends in Rotor Dynamics (IUROTOR-2009), March 23-26, 2009, Indian Institute of Technology Delhi, India. (ISI/SCOPUSCited Publication)

Proceeding IUTAM Symposium on Emerging Trends in Rotor Dynamics (IUROTOR-

2009), March 23-26, 2009, Indian Institute of Technology Delhi, India. (ISI/SCOPUSCited Publication)

1982

LALWANI, R. K. (ISI-Cited Publication)

1971

Lalwani, R. J. (ISI-Cited Publication )

AREAS OF RESEARCH(Project title), (Role), (From)-(Until), (Source), (Level).

LARGE DEFLECTION, THERMO-MECHANICAL ANALYSIS AND SIMULATIONOF FUNCTIONALYY GRADED PIEZOELECTRIC PIPES BASED ON SHEARDEFORMATION THEORY, Principal Investigator(PI), 2010-2011


3/25

CONSULTATION PROJECT/CONSULTANCY(Project title), (Role), (From)-(Until), (Organisation).

Dynamic Analysis of Water Turbine, Project Leader, Skyline Institute of Engineering andTechnology

AWARDS AND RECOGNITIONS(Name of Award), (Awarding Institution), (Year Awarded), (Level).

Best Speaker Award, MAULANA AZAD NATIONAL INSTITUTE OF TECHNOLOGY,1982

HSIEH-CHIH ASSOCIATION AWARD, TATUNG INSTITUTE [NOW UNIVERSITY]OF TECHNOLOGY, 1989

PRESENTATIONS(Title), (Event), (Date Presented), (Organiser), (Level).

Presenter

Role of Research and Morality in Quality Learning in Higher Education., InternationalCONFERENCE ON TEACHING AND LEARNING IN HIGHER EDUCATION 2009,13 Nov 2009 to 13 Nov 2009, ICTLHE09

Role of IT in Educational Institutes, Role of IT in Educational Institutes , March 17-18,2001, Fifth Annual Convention of ISTE (M.P.), National Seminar on Impact of

Information Technology in Technical Education, Indore, India, 17 Mar 2001 to 17 Mar2001, Indian Society for Technical Education, Bhopal., (National)

Problems and Issues in Realizing Sustainable Development In Higher Education ThroughSoft and Hard Skills, THE 3RD INTERNATIONAL CONFERENCE OF UNESCOCHAIR HIGHER EDUCATION FOR SUSTAINABLE DEVELOPMENT (HESD):TRANSFORMING HIGHER EDUCATION FOR A SUSTAINABLE SOCIETY, 20-22

NOVEMBER 2009, USM, PENANG, MALAYSIA., 21 Nov 2009 to 21 Nov 2009,USM, PENANG, MALAYSIA., (International)

(b)Rotor Fault Detection in Machines: Methods and Techniques, IUTAM Symposium onEmerging Trends in Rotor Dynamics (IUROTOR-2009), March 23-26, 2009, IndianInstitute of Technology Delhi, India., 25 Mar 2009 to 25 Mar 2009, Indian Institute ofTechnology Delhi, India., (International)

On Condition Machine Health Monitoring Against Corrosion., World CORCON 2009"International Conference & Expo on Corrosion during 29th Sept. - 1st Oct 2009 atMumbai, 30 Sep 2009 to 30 Sep 2009, World CORCON 2009, (International)

SUPERVISION


4/25

Post Graduate Level(Name of Degree), (Name of Candidates), (Title of Thesis), (Academic Session), (Status)

Master Degree, Lee, FINITE ELEMENT ANALYSIS OF SPUR GEAR TOOTH,1989/1990, Completed

Master Degree, Sajjad Zarghan, VIBRATIONAL ANALYSIS OF TAPPEREDCRACKED SHAFT, 2009/2010, Ongoing

TEACHING(Course Title), (Academic Session), (No of Student), (No of Contact Hours).

First Degree

COMPUTATIONAL MATERIAL ENGINEERING, 2009/2010(1), 21, 72

MECHANICS OF APPLIED MATERIALS, 2009/2010, 61, 72

NON-FERROUS ALLOY, 2009/2010(2), 60, 52

FLUID DYNAMICS, 2007/2008(2), 100, 98

EVALUATION ACTIVITIES(Description), (Evaluation Activity).

Under graduate, Post gradute and Ph.D. Theses and viva presentation, Thesis

Effect of Nickel and Cobalt Nanoparticle additions to Sn-Ag-Cu Solder, Thesis

BIOGRAPHY

Prof. Ramesh Kumar Lalwani received his PhD in 1972 from IndianInstitute of Technology, Kharagpur based on his doctoral thesis titled"Noise and Vibrations generated by Ball Bearings". For the next two years,he led the research group on "Elastic Wave Propagation in rods" at theinstitute fur Mekanik at Technical University Hannover, Germany. In 1975he participated at International Centre for Mechanical Sciences, Udine,Italy. In 1976 he was appointed as expatriate visiting faculty at Universityof Benin, Benin City. In 1981 he joined as Head of Agriculture EngineeringDepartment at the Federal University of Technology, Makurdi. He was thenappointed as the dean of the Faculty of Engineering at University of Jos, Josin 1985. In 1986 he was selected to join Tatung University of Technology,


5/25

Taipei, Taiwan where as Professor and consultant to Tatung Company hecontributed in many research projects and publication along with teachingand guiding post graduate students. In 1989 was awarded with a citationwhich states " Professor Ramesh Kumar Jamnadas Lalwani of TatungInstitute of Technology has devoted himself to scholastic research and

published many outstanding papers in different academic journals. We arehereby honored, in recognition of his great contributions to Science andTechnology, to present him this Hsieh-Chih Association Award". In 1991he joined Gajra Bevel Gears, Dewas as their ISO-9001 consultant. In 1992he was appointed as the Principal of A. C. College of Engineering,Sangamner. Since then he has been working in many Indian Institutes ofTechnical education. He has published 3 books, many memo-graphs, andresearch papers. He is a life member of Indian Society for TechnicalEducation and Fellow of the Institute of Engineers [India}, Member ofInternational NFPA, USA.Since 2009 he is professor of Mechanical Engineering in top Malaysian and

among the top 180 universities of the World the University of Malaya.

Elastic behavior of glass-like functionallygraded infinite hollow cylinder underhydrostatic loads using finite element method

R. Afshar, a,

, M. Bayata,

, R.K. Lalwania

and Y.H. Yaua

a Mechanical Engineering Department, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 16 March 2010;

accepted 19 July 2010.

Available online 24 July 2010.

Abstract

A glass-like (viscoelastic) functionally graded cylinder is studied by using finite element methodto investigate the mechanical responses. A subroutine is developed by using ANSYS parametric

design language (APDL) to simulate two nonlinearities, which are the variation of material

properties with respect to time and position. The cylinder is made of two different viscoelastic

materials, namely, pure material one at inner and pure material two at outer surfaces. The


6/25

material properties are assumed to be presented by simple power law distribution and moreover,

bulk and shear moduli are varying with respect to time using the kernel functions depicted

regarding Prony series. It is shown that the hoop stresses take the same values at the mean radius

(middle of the thickness) for different values of time and grading index. It is found that the radial

stress decreases to certain values for specific grading index and then by increasing the grading

index it increases to maximum value that related to pure material cylinder. It is shown that unlike

the zero axial stress in pure material cylinders, it varies along the thickness from minimum to

maximum at inner and outer surfaces, respectively. It is concluded that the viscoelastic

functionally graded (VFG) materials play an important role in steady and transient response of

hollow cylinder under hydrostatic load.

Keywords: A: Glass-like functionally graded materials; E: Mechanical response; F: Elasticbehavior

Article Outline

1.Introduction

2.Gradation relations

2.1. Viscoelastic material properties2.1.1. Constitutive equations

2.2. Functionally graded materials (FGMs)

3.Numerical method

3.1. Material properties

3.2. Element types

4.

Boundary conditions5.Numerical results for the case study and discussion5.1. Results and discussion

6.Conclusions


7/25

References

1. Introduction

A material with elastic and viscous parts is defined as viscoelastic material. Generally,

viscous property changes with respect to time, whereas the elastic deformation occursinstantaneously due to applied load. The brittle materials such as glass or glass-like

materials by having different properties due to heating and cooling process can be

modeled as viscoelastic materials [1], [2] and [3]. The brittle materials with high values

of modulus of elasticity can be applied to reinforce the pure metal structures. This

arrangement of two different materials introduces advance material named functionally

graded materials (FGMs). FGMs are combination of at least two materials which vary

smoothly as a function of location along certain dimension(s) of the structure by

considering variation of volume fraction of components [4], [5], [6], [7] and [8].

Application of FGMs can be seen in pipes in oil and gas industry, under water

equipments, aerospace instruments, storage cylinders, hollow rotating shafts and

winding of composite pressure vessels and so on. Because of increasing application of

FGMs and viscoelastic materials, new methodologies need to be developed to

characterize, analyze and design structural components made of these materials.

A number of investigations dealing with mechanical loads like hydrostatic, dynamic as

well as thermal loads have been published in the scientific literature [9], [10], [11] and[12]. In recent years, Vinogradov and Milton [9] studied the creep of a composite

consist of two linear viscoelastic materials and subjected to a constant hydrostatic or

anti-plane loading. Aydlner and stndag [10] investigated the residual stresses in a

bulk metallic glass cylinder. They induced thermal tempering to the model and

analyzed the stress generation. Lee [11] examined the thermomechanical response of a

viscoelastic thin-walled cylinder under instant internal pressure while uniform

temperature increased gradually by using a time-domain boundary element analysis.

Seoudi et al. [12] solved the two-dimensional elastic wave equations of the viscoelastic

cylinders to investigate the periodic deformations of the cylinders. Golden and Graham

[13] studied a dynamic response of viscoelastic rolling cylinder using the non-inertial

approximation. Different types of advanced materials are used for cylindrical shapes

for different purpose, for example biological tissues with viscoelastic behavior in


8/25

biomechanics field as well as functionally graded (FG) cylinder used in oil and gas

transportation.

Many studies have been done FG cylinders due to internal pressure [14], [15], [16],

[17], [18], [19] and [20]. Sepiani et al. [14] studied the cylinders with combination of

FG and pure material shell as inner and outer, respectively, to obtain the free vibration

and buckling results while cylinders subjected to fatigue loads. Theoretical

formulations were obtained based on First-order shear deformation theory and their

results were verified with numerical method. Hosseini [15] applied Galerkin Finite

Element (FE) to investigate the coupled thermoelastic behavior of FG thick hollow

cylinder. The dynamic behavior as well as thermomechanical response were obtained.

Later, Shahabian and Hosseini [16] applied the same procedure such as [15] as well as

Monte Carlo simulation to study a dynamic behavior of a FG thick hollow cylindersubjected to shock loading. A non-linear power function of radius was assumed for

variation of the mechanical properties along the thickness of structure. Batra and

Laccarino [17] found elasticity solutions for displacement field in a long FG cylinder

subjected to hydrostatic pressure. The material properties were assumed an isotropic

and incompressible second-order elastic material with modulus varying only in the

radial direction. Huang and Han [18] considered a long FG cylindrical shell to describe

post-buckling behavior and also the non-linear buckling subjected to axial compression

and lateral loads. They employed Ritz energy method to present the non-linear large

deflection. The numerical results showed various effects of the inhomogeneous

parameter, dimensional parameters and external thermal environments. In another

study, Batra and Bahrami [19] investigated the radial deformation of a FG hollow

cylinder under internal pressure. MooneyRivlin material model was considered to

describe the material properties. Shen [20] studied a FG cylindrical shell under torsion

loading to analyze post-buckling behavior in thermal environment. A higher order

shear deformation theory was used for the governing equations. The results revealed

that distribution of the volume fraction of FGMs has a noteworthy effect on the

buckling load and post-buckling behavior of FGM cylindrical shells under torsion.

However, for some specific application such as in biomechanics and aerospace where

high toughness, light weight and durability becomes crucial, the components need to be


9/25

fabricated using special material such as a viscoelastic functionally graded materials

(VFGMs).

Many studies on VFGMs have been reported [21], [22], [23], [24], [25], [26], [27],

[28] and [29]. Khan and Muliana [21] presented a micromechanical-structural

framework to analyze VFGMs under thermomechanical loads. They compared the

experimental and numerical result. Panda and Ray [22] investigated a FG laminated

composite plates integrated with a patch of active constrained viscoelastic layer

damping treatment to obtain the non-linear dynamic response. Pan et al. [23] studied

the fracture analysis of a viscoelastic functionally graded (VFG) strip. Parameters such

as material grading index, crack length and spacing as well as the loading condition on

the crack tip field intensity factor were investigated. A micromechanical model was

introduced by Muliana [24] for predicting effective thermal behaviors of VFGMs.Experimental data as well as analytical solutions in the literatures were used for

verification of their work. Khazanovich [25] showed the compatibility of elastic

viscoelastic correspondence principle for non-homogeneous materials with separable

relaxation modulus. Gilhooley et al. [26] used the meshes local PetrovGalerkin

(MLPG) procedure to simulate a two-dimensional static and dynamic deformation of

VFGMs. Bhangale and Ganesan [27] used the finite element method (FEM) to study

the bucking and vibration behavior of a VFG beam in thermal environment. Hilton [28]

modeled FGMs structure as non-homogenous material and investigated viscoelastic

and elastic behavior of the structure. In another study, Sladek et al. [29] analyzed two-

dimensional anisotropic and linear VFG solids by using the MLPG approach.

Moreover, he verified the accuracy of the proposed method.

It can be noted that the existing literature on viscoelastic and FG cylinders as well as

VFGMs structures, to the best of authors knowledge, a very limited and little work has

been done that analyzed VFG long cylinder under hydrostatic load. This very fact

motivates the investigation of the present study. This study attempts to consider an

axisymmetric model of long thick-walled cylinder of inner radius Ri and outer radius

Ro subjected to internal hydrostatic pressure,Pi (Fig. 1). The viscoelastic material

properties of the FG cylinder are varying along the thickness based on a simple power

law distribution in terms of the volume fractions of the constituents (detail A in Fig. 1


10/25

illustrates the number of layers along the thickness of the cylinder). FEM is used in

ANSYS environment to obtain radial deformation and stress as well as hoop stress for

various materials grading index (MGI). A subroutine is developed using APDL. The

cylinder is made of two different materials at the outer and inner surfaces to investigate

the effect of gradual variation of material properties. Viscoelastic parameters, bulk and

shear moduli, are varying with respect to time using the kernel functions depicted

regarding Prony series while they are function of radial position by using power law

distribution.

Full-size image (31K)

Fig. 1. Configuration of a long VFG cylinder.

View Within Article

2. Gradation relations

2.1. Viscoelastic material properties

2.1.1. Constitutive equations

Based on infinitesimal theory, in the range of fast and slow applied load, elastic

response can be calculated by the Caushy stress () as:

(1) where G(t),K(t), e, , t, and Iare shear relaxation kernel function, bulk relaxation kernel function, deviatoric part of

the strain, volumetric part of the strain, current time, past time and unit tensor,

respectively.


11/25

For the element used in this analysis (PLANE183) the kernel functions areKand G

depicted regarding Prony series, which assumes that:

(2) where

K,Ki, , and Gi are bulk elastic, moduli shear relaxation times elastic moduli

for each Prony component and trepresents the current time. The number of Prony

terms for shear is nG and for volumetric behavior is nK. The relaxation behavior of the

deviatoric and volumetric portions of the stress is different. It is worth mentioning that

the value ofnG, nK, and can be different.

The relative moduli are introduced as:

(3) where and

.

The kernel functions can be equivalently expressed as:

(4) Here, G0, G andK0,K, are the shear

and bulk moduli at the fast and slow load limit, respectively.

2.2. Functionally graded materials (FGMs)

In this study, the property variation, M, of the material in the VFG cylinder along the

radial direction is assumed based on power law distribution of the following form [4]:

(5) Here Mi and Mo are the

material properties of inner and outer surfaces of hollow cylinder, respectively, Mo is


12/25

the material property of pure material one and Mi is the material property of pure

material two; n 0 is the gradation index.

3. Numerical method

The basis of simulation has been carried out by using ANSYS finite element package.

The following section describes in detail the steps involved in using the software for

analysis of VFG cylinder.

3.1. Material properties

The mechanical properties needed are modulus of elasticity, Eand Possions ratio, .

Two Proney series in representation of viscoelastic behavior are specified using TB

and TBDATA commands in ANSYS.

3.2. Element types

An axisymmetric 2-D eight-noded PLANE183 element is used (Fig. 2). Two types of

PLANE183 with eight or six nodes with quadratic displacement behavior can be used.

And also, the option of plane stress or plane strain can be applied for the axisymmetric

models in this element. In the axisymmetric case, Yaxis is the axis of symmetry [1].


Fig. 2. PLANE183 element geometry [1].

View Within Article

For the purpose of simulation, the long cylinder is divided into a number of divisions in

radial direction. Each of the divisions has its own material properties in accordance

with power law distribution in the radial direction as it is mentioned in Eq. (5). The

material properties of the FG cylinder are evaluated at the element centroid. ANSYS

Parametric Design Language (APDL) is used.

Fig. 3 shows the flowchart of simulation of VFG cylinder.


13/25


Fig. 3. Flowchart of computational scheme.

View Within Article

4. Boundary conditions

The VFG cylinder is subjected to inner pressure ofPi as shown in Fig. 1. The

following traction boundary conditions on the hollow cylinder must be satisfied:

where Ua and r are axial displacement and radial stress,

respectively.

5. Numerical results for the case study and discussionFor numerical illustration of the non-linear elastic solution of this study, a hollow

viscoelastic cylinder with Ri/Ro = 0.5 and thickness of 2 (50 mm), subjected to

internal pressure of 1 Psi (6895 Pa) is considered. The cylinder is long in the out-of-

plane,Z, direction. The axisymmetric model of the cylinder with applied loads and

boundary conditions is depicted in Fig. 4.



14/25

Fig. 4. Axisymmetric model of the cylinder.

View Within Article

In the following section, results are presented by considering simple case of Eq. (1)

where the shear and bulk moduli of the viscoelastic cylinder behave as:

(6-A)

(6-B) In which G0 andK are defined as

G0 = Ei/(1 + 2c),K = Ei/[3(1 + 2c)] for inner surface and G(0) = G0 = Eo/(1 + 2c),

K0 = Eo/[3(1 + 2c)] for outer surface. The elastic moduli of inner and outer surface are

assumed Ei = 105 Psi (689.5 MPa) and Eo = 20 105 Psi (13789.5 MPa), respectively.The Poissons ratio is constant (c = 1/3).

For more specific to adjust parameters in ANSYS by considering the viscoelastic

material behavior as:

(7) In

accordance with Eq. (6-A), the parameters in Eq. (7) take the following values:

The material properties are given in Table.

1.

Table 1.

Material properties used for case study.

Material property E (MPa) G1/G0 K1/K0 G/K


15/25

Material property E (MPa) G1/G0 K1/K0 G/K

Pure material one (inner surface) 689.5 0.3 1 0.0 1.0

Pure material two (outer surface) 13789.5 0.3 0.5 0.5 2.0

Full-size tableView Within Article

In this section, results are presented in non-dimensional form normalizing stresses and

radial displacement by factors Eo andRo, respectively. Moreover, the presented method

and results in the following section may be verified by comparing the numerical results

presented in [Fig. 7], [Fig. 9], [Fig. 10] and [Fig. 12]. These comparing and validating

will be a part of our study numerical results reported in the following section.


Fig. 7. Variation of non-dimensional hoop stress (h/Eo) of VFG long cylinder for

specific grading index n = 0.8 at different times.

View Within Article


Fig. 9. Variation of non-dimensional radial displacement (Ur/Ro) in VFG long

cylinder for different grading index at the end of solution time (t= 10 (s)).

View Within Article


16/25


Fig. 10. Variation of non-dimensional radial stress (r/Eo) for different grading index

in VFG long cylinder at t= 10 (s).

View Within Article


Fig. 12. Variation of non-dimensional axial stress (a/Eo) for different grading index


View Within Article

5.1. Results and discussion

Fig. 5 illustrates the non-dimensional radial displacement in VFG long cylinder fordifferent times and grading index n = 0.8.


Fig. 5. Variation of non-dimensional radial displacement (Ur/Ro) in VFG long

cylinder for different times and grading index n = 0.8.

View Within Article


17/25

It can be seen that the radial displacement decreases along the thickness of the VFG

cylinder from inner towards outer. It is observed that the radial displacement increases

with the increase of the time. It is evident that the slope of decreasing radial

displacement increases with respect to time at the certain position. And also the slope

of radial displacement versus radius close to outer surface tends to zero. This

phenomenon can be explained by interaction between material behavior such as

viscoelastic and FGMs by considering the boundary conditions. As expected the inner

displacements are greater than those at outer surface.

Fig. 6 presents the non-dimensional radial stress in VFG long cylinder for different

times and grading index n = 0.8.


Fig. 6. Variation of non-dimensional radial stress (r/Eo) in VFG long cylinder for

different times and grading index n = 0.8.

View Within Article

Fig. 6 shows the decrease of radial stress along the thickness of the cylinder from inner

towards outer surface. As expected, the value of radial stress is zero at outer surface

because of non-loading condition. Furthermore, the slope of radial stress decreases

with respect to time at the certain position. It is worth to mention that by increasing the

time the shape of variation radial stress along the thickness changes from concave to

convex.Fig. 7 demonstrates the non-dimensional hoop stress of VFG long cylinder for specific

grading index n = 0.8 in different times. Comparing with the results ofFig. 8 in [30], it

can be said that the hoop stresses for the FG cylinder has the same value at certain

point and the dimensionless hoop stresses increase by increasing the time at outer

surface in contract to behavior at inner surface.


18/25


Fig. 8. Variation of non-dimensional axial stress (a/Eo) of VFG long cylinder for

specific grading index n = 0.8 in different times.

View Within Article

It is noticed that the hoop stresses decrease with the increase of time at each point

while R/Ro < 0.75. Whereas, the hoop stresses increase with respect to time when

R/Ro > 0.75. The slope of hoop stress decreases from inner towards outer surface. It can

be noted that the value of hoop stress for different times is the same at middle of the

thickness.

Fig. 8 depicts the variation of non-dimensional axial stress in VFG long cylinder for

specific grading index n = 0.8 at different times while the inner pressure is applied.

It can be explained that the behavior of variation of axial stresses is the same as that for

hoop stress as shown in Fig. 7. It is noticed that the axial stress gets the same valuebefore the middle of thickness 0.7 < R < 0.75. This phenomenon can be explained by

interaction between viscoelastic as well as FGMs behavior. It is worth mentioning that

the axial stress is negative close to inner surface while there is tensile stress close to

outer surface. This behavior can be justified by presentence of harder material at outer

surface for reinforcing the cylinder.

Fig. 9 illustrates the non-dimensional radial displacement in VFG long cylinder for

different grading index at the end of solution time (t= 10 (s)).

It can be observed that the radial displacement increases with increase of grading

index, n, from zero to (pure material 1) up to its maximum value forn (pure

material 2). It is noticed that the results for VFG cylinder lie in between pure material

cylinders. It can be seen that the radial displacement decreases along the thickness of

the VFG cylinder from inner towards outer for all values of grading index. It is evident


19/25

that the slope of decreasing radial displacement increases with increase of grading

index at the certain position. And also the variation of radial displacement close to

outer surface tends to zero for all grading indexes. It has been noticed from numerical

simulations that radial displacement in pure viscoelastic cylinder (material 1) is greater

than others. Then, in order to show clearly the effect of different values of grading

index (n) the results for pure viscoelastic cylinder (material 1) has not been drawn in

Fig. 9. This result can be validated with the one reported earlier[31], FG cylinder

under radially symmetry loads.

Fig. 10 shows the non-dimensional radial stress for different grading index in VFG

long cylinder at t= 10 (s)

It can be noted that the radial stresses for pure material are the same while the results

for VFG cylinder are smaller than those for pure material cylinders. It is seen that byincreasing the value of grading index, n, the radial stresses decrease to certain values

for certain grading index, n, then increase to pure material cylinder again. These results

confirm accepted results for free boundary condition at outer, that means, stress is zero

where R = Ro. Yet again, the behavior of variation of radial stresses for different times

(Fig. 6) are the same as those for different grading index (Fig. 10). It is indeed when

one considers the pure viscoelastic cylinder (materials 1 or 2), the values of the radial

stresses take the same value and also greater than those for VFG cylinders. Fig. 3 in

Ref. [31] also validates our solution for FG cylinder since the compressive stresses

through out the thickness reach to zero at outer surface by changing the grading index.

Fig. 11 demonstrates the non-dimensional hoop stress for different grading index in

VFG long cylinder at t= 10 (s).



20/25

Fig. 11. Variation of non-dimensional hoop stress (h/Eo) for different grading index


View Within Article

It can be seen that the hoop stress for pure material decreases along the thickness of the

cylinder. Furthermore, hoop stress increases by increasing grading index close to outer

surface. It is worth to mention that maximum hoop stress for pure material cylinders

occurs at inner while it occurs at outer surface for FG cylinders. It is seen that the hoop

stress in FG cylinder are less than those in pure material cylinder close to inner surface

in contrast of its behavior close to outer surface.

Fig. 12 illustrates the non-dimensional axial stress for different grading index in VFG

long cylinder at t= 10 (s).It is seen that the axial stress in pure material cylinder remains constant along the

thickness unlike its behavior for VFG cylinder. Furthermore, close to outer surface,

axial stress increases by increasing grading index. It is worth to mention that maximum

and minimum axial stress in VFG cylinder occurs at outer and inner surfaces,

respectively. The presented results can be verified by comparing the axial stresses for

pure material cylinder with the given formula in chapter 11 and Eq. (11.19) by Boresi

and Schmidt [32] as:

(8) It is interesting to mention that the

results for pure viscoelastic cylinder without thermal load (T) are zero. It can be said

that the general behavior of axial and hoop stress for VFG cylinders are similar to each

other.

6. ConclusionsA stress analysis of viscoelastic functionally graded (VFG) cylinders is implemented

by using finite element method (FEM). The conclusions from the present study for

VFG cylinder can be summarized as follows:

For all time and grading index, the radial displacement takes constant values close to

outer surface when the values of grading indexes (n) are smaller than one. Moreover,


21/25

contrary to the results for radial stress, hoop stress can take the positive values

throughout the thickness in different times. Also, the curve of radial stress is convex

unlike hoop stress at all times. The hoop stresses cross each other around the mean

thickness (R/Ro 0.75) at different times, while, this phenomena occurs before mean

thickness (R/Ro 0.725) for axial stresses. The behavior of axial and hoop stress are

the same unlike the radial stress that is always compressive for different time. Unlike

VFG cylinders, maximum hoop stress for pure cylinders takes place at inner surface.

Furthermore, maximum hoop stress in VFG cylinders happens at outer surface while

there is the minimum hoop stress for pure cylinder.

References

[1] ANSYS 11, Users manual. ANSYS Corporation Inc.; 2008.

[2] D. Blend, The linear theory of viscoelasticity, Pergamon Press, New York (1960).

[3] A.D. Drozdov, Mechanics of viscoelastic solids, John Wiley & Sons, Ltd., UK

(1998).

[4] M. Bayat, B.B. Sahari and M. Saleem, Bending analysis of a functionally graded

rotating disk based on the first order shear deformation theory, ApplMathModel33

(11) (2009), pp. 42154230. Article | PDF (710 K) | View Record in Scopus | Cited

By in Scopus (2)

[5] M. Bayat, B.B. Sahari and M. Saleem, Thermoelastic solution of a functionally

graded variable thickness rotating disk with bending based on the first-order shear

deformation theory, Thin-Wall Struct47 (5) (2009), pp. 568582. Article | PDF

(922 K)

[6] M. Bayat, M. Saleem and B.B. Sahari, Thermo elastic analysis of a functionally

graded rotating disk with small and large deflections, Thin-Wall Struct45 (78) (2007),

pp. 677691. Article | PDF (290 K) | View Record in Scopus | Cited By in Scopus

(5)


22/25

[7] Y. Fukui and N. Yamanaka, Elastic analysis for thick-walled tubes of functionally

graded material subjected to internal pressure, JSME IntJ35 (4) (1992), pp. 379385.

View Record in Scopus | Cited By in Scopus (35)

[8] S. Suresh and A. Mortensen, Fundamental of functionally graded materials, IOM

Communication Limited, UK (1998).

[9] V. Vinogradov and G.W. Milton, The total creep of viscoelastic composites under

hydrostatic or antiplane loading, JMech Phys Solids53 (6) (2005), pp. 12481279.

Article | PDF (507 K) | View Record in Scopus | Cited By in Scopus (5)

[10] C.C. Aydlner and E. stndag, Residual stresses in a bulk metallic glass cylinder

induced by thermal tempering, MechMater37 (1) (2005), pp. 201212.

[11] S.S. Lee, Boundary element analysis of a viscoelastic thin-walled cylinder

subjected to thermal transient,IntJPress Ves Pip63 (2) (1995), p. 195. Article |

PDF (347 K)Article | PDF (583 K) | View Record in Scopus | Cited By in Scopus

(2)

[12] B.M. Seoudi, V.M. Kulik and A.V. Boiko, New approach to the computation of

the form factor of viscoelastic cylinders, MechMater41 (5) (2009), pp. 495505.

Article | PDF (924 K) | View Record in Scopus | Cited By in Scopus (0)

[13] J.M. Golden and G.A.C. Graham, The problem of a viscoelastic cylinder rolling

on a rigid half-space, Math ComputModel34 (1213) (2001), pp. 13631397. Abstract

| PDF (1682 K) | View Record in Scopus | Cited By in Scopus (0)

[14] H.A. Sepiani, A. Rastgoo and F. Ebrahimi, Vibration and buckling analysis oftwo-layered functionally graded cylindrical shell, considering the effects of transverse

shear and rotary inertia, MaterDes31 (3) (2010), pp. 10631069. Article | PDF

(649 K) | View Record in Scopus | Cited By in Scopus (1)


23/25

[15] S.M. Hosseini, Coupled thermoelasticity and second sound in finite length

functionally graded thick hollow cylinders (without energy dissipation), MaterDes30


By in Scopus (4)

[16] F. Shahabian and S.M. Hosseini, Stochastic dynamic analysis of a functionally

graded thick hollow cylinder with uncertain material properties subjected to shock

loading, MaterDes31 (2) (2010), pp. 894901. Article | PDF (623 K) | View

Record in Scopus | Cited By in Scopus (1)

[17] R.C. Batra and G.L. Iaccarino, Exact solutions for radial deformations of a

functionally graded isotropic and incompressible second-order elastic cylinder,IntJ

Non-LinearMech43 (5) (2008), pp. 383398. Article | PDF (489 K) | View Record

in Scopus | Cited By in Scopus (8)

[18] H. Huang and Q. Han, Nonlinear buckling and postbuckling of heated functionally

graded cylindrical shells under combined axial compression and radial pressure,IntJ

Non-LinearMech44 (2) (2009), pp. 209218. Article | PDF (1223 K)Article |

PDF (342 K) | View Record in Scopus | Cited By in Scopus (4)

[19] R.C. Batra and A. Bahrami, Inflation and eversion of functionally graded non-

linear elastic incompressible circular cylinders,IntJNon-LinearMech44 (3) (2009),

pp. 311323. Article | PDF (594 K) | View Record in Scopus | Cited By in Scopus

(5)

[20] H.S. Shen, Torsional buckling and postbuckling of FGM cylindrical shells in

thermal environments,IntJNon-LinearMech44 (6) (2009), pp. 644657. Article |

PDF (585 K) | View Record in Scopus | Cited By in Scopus (1)

[21] K.A. Khan and A.H. Muliana, A multi-scale model for coupled heat conduction

and deformations of viscoelastic functionally graded materials, Compos Part B: Eng40


24/25

(6) (2009), pp. 511521. Article | PDF (946 K) | View Record in Scopus | Cited By

in Scopus (0)

[22] S. Panda and M.C. Ray, Active control of geometrically nonlinear vibrations of

functionally graded laminated composite plates using piezoelectric fiber reinforced

composites, JSound Vib325 (12) (2009), pp. 186205. Article | PDF (1438 K) |

View Record in Scopus | Cited By in Scopus (3)

[23] F. Pan, W. Li and B. Wang, Viscoelastic fracture of multiple cracks in

functionally graded materials, ComputMethods ApplMechEng198 (3336) (2009),

pp. 26432649. Article | PDF (901 K) | View Record in Scopus | Cited By in

Scopus (1)

[24] A.H. Muliana, A micromechanical model for predicting thermal properties and

thermo-viscoelastic responses of functionally graded materials,IntJSolids Struct46


By in Scopus (1)

[25] L. Khazanovich, The elasticviscoelastic correspondence principle for non-

homogeneous materials with time translation non-invariant properties,IntJSolidsStruct45 (17) (2008), pp. 210.

[26] D.F. Gilhooley, J.R. Xiao and R.C. Batra, Two-dimensional stress analysis of

functionally graded solids using the MLPG method with radial basis functions, Comput

MaterSci41 (4) (2008), pp. 467481. Article | PDF (3122 K) | View Record in

Scopus | Cited By in Scopus (7)

[27] R.K. Bhangale and N. Ganesan, Thermoelastic buckling and vibration behavior of

a functionally graded sandwich beam with constrained viscoelastic core, JSound Vib

295 (12) (2006), pp. 294316. Article | PDF (632 K) | View Record in Scopus |

Cited By in Scopus (13)


25/25

[28] H.H. Hilton, Optimum linear and nonlinear viscoelastic designer functionally

graded materials characterizations and analysis, Compos PartA: Appl Sci Manuf36


By in Scopus (3)

[29] J. Sladek, V. Sladek and C. Zhang, Stress analysis in anisotropic functionally

graded materials by the MLPG method, EngAnalysis BoundElem29 (6) (2005), pp.

597609. Article | PDF (269 K) | View Record in Scopus | Cited By in Scopus (8)

[30] Z.S. Shao and G.W. Ma, Thermo-mechanical stresses in functionally graded

circular hollow cylinder with linearly increasing boundary temperature, Compos Struct

83

(3) (2008), pp. 59265.

[31] M. Jabbari, S. Sohrabpour and M.R. Eslami, Mechanical and thermal stresses in a

functionally graded hollow cylinder due to radially symmetric loads,IntJPress Ves

Pip79 (7) (2002), pp. 493497. Article | PDF (159 K) | View Record in Scopus |

Cited By in Scopus (75)

[32] A.P. Boresi and R.J. Schmidt, Advanced mechanics of materials (6th ed.), John

Wiley & sons Inc., USA (2002).

Rkl Um 2010 Curriculum Vitae

Documents

Transcript of Rkl Um 2010 Curriculum Vitae