DESIGN AND ANALYSIS OF FUNCTIONALLY GRADED … · Keyword: Functional Graded Material Analysis, Buckling Analysis Cite this Article: M. Shunmugasundaram, D.Maneiah and CH.Nagaraju,

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International Journal of Mechanical Engineering and Technology (IJMVolume 9, Issue 11, November 201

Available online at http://www.iaeme.com/ijm

ISSN Print: 0976-6340 and ISSN Online: 0976

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DESIGN AND ANALYSIS

GRADED CYLINDRICAL S

STATIC AND BUCKLING

M. Shunmugasundaram,

Department of Mechanical Engineering,

CMR Technical Campus, Hyderabad, Telangana, India

ABSTRACT

Thin cylinders shells are highly efficient structures which have wide variety

applications in the field of Mecha

chemical Industries etc.. The ratio of the wall thickness to diameter should be

1/15. Their strength is limited by Buckling and vibration. Cylindrical shells

generally in used for storage of fue

composite materials. Due to heavy load at the

deformation by the process of delamination.

Graded Material (FGM) is

belongs to a class of advanced material characterized by

dimension direction. This study is used to investigate the

and vibration. The analysis result shows that

suitable for the space fuel tank.

Keyword: Functional Graded Material

Analysis, Buckling Analysis

Cite this Article: M. Shunmugasundaram, D.Maneiah and CH.Nagaraju, Design and

Analysis of Functionally Graded Cylindrical Shell by Applying Static and Buckling

Load, International Journal of Mechanical Engineering and Technology, 9(11), 2018,

pp. 1808–1821.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=1

1. INTRODUCTION

In The term FGM was originated in the mid

Functionally graded materials (FGM’s) are a new generation of

the micro structural details are spatially varied

reinforcement phases to suit particular

reinforcements with different

roles of the reinforcement and matrix phases in a continuous manner. Functionally graded

materials (FGMs) are composite materials formed of two or more constituent

IJMET/index.asp 1808 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET) 2018, pp. 1808–1821, Article ID: IJMET_09_11_

http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=

6340 and ISSN Online: 0976-6359

Scopus Indexed

DESIGN AND ANALYSIS OF FUNCTIONALLY

GRADED CYLINDRICAL SHELL BY APPLYING

STATIC AND BUCKLING LOAD

hunmugasundaram, D.Maneiah and CH.Nagaraju

Department of Mechanical Engineering,

CMR Technical Campus, Hyderabad, Telangana, India

Thin cylinders shells are highly efficient structures which have wide variety

applications in the field of Mechanical, Civil, Aerospace, Marine, Power Plant,

chemical Industries etc.. The ratio of the wall thickness to diameter should be

1/15. Their strength is limited by Buckling and vibration. Cylindrical shells

generally in used for storage of fuel. Now a day’s space craft fuel tank

composite materials. Due to heavy load at the top surface, the structures undergo

deformation by the process of delamination. In this proposed study,

(FGM) is used to eliminate the delamination problem. The

belongs to a class of advanced material characterized by variation in properties in the

dimension direction. This study is used to investigate the behavior of stress, buckling

The analysis result shows that the proposed material is one of the

suitable for the space fuel tank.

Functional Graded Material, Thin Cylindrical Shell, ANSYS

Analysis, Buckling Analysis.

M. Shunmugasundaram, D.Maneiah and CH.Nagaraju, Design and


, International Journal of Mechanical Engineering and Technology, 9(11), 2018,


The term FGM was originated in the mid-1980s in Japan by a group of

Functionally graded materials (FGM’s) are a new generation of engineered materials wh

the micro structural details are spatially varied through non-uniform distribution of the

reinforcement phases to suit particular applications. Engineers accomplish this by using

reinforcements with different properties, sizes and shapes as well as by interchanging the

reinforcement and matrix phases in a continuous manner. Functionally graded

materials (FGMs) are composite materials formed of two or more constituent

[email protected]

_188

ET&VType=9&IType=11

OF FUNCTIONALLY

HELL BY APPLYING

LOAD

and CH.Nagaraju

Thin cylinders shells are highly efficient structures which have wide variety of

nical, Civil, Aerospace, Marine, Power Plant, Petro

chemical Industries etc.. The ratio of the wall thickness to diameter should be above

1/15. Their strength is limited by Buckling and vibration. Cylindrical shells are

space craft fuel tank is made up of

top surface, the structures undergo

In this proposed study, Functionally

delamination problem. The FGM

variation in properties in the

behavior of stress, buckling

the proposed material is one of the

ANSYS, Stress

M. Shunmugasundaram, D.Maneiah and CH.Nagaraju, Design and


, International Journal of Mechanical Engineering and Technology, 9(11), 2018,


1980s in Japan by a group of scientists.

engineered materials wherein

uniform distribution of the

applications. Engineers accomplish this by using

y interchanging the

reinforcement and matrix phases in a continuous manner. Functionally graded

materials (FGMs) are composite materials formed of two or more constituent phases with a

M. Shunmugasundaram, D.Maneiah and CH.Nagaraju

http://www.iaeme.com/IJMET/index.asp 1809 [email protected]

continuously variable composition. The composition is varied from a ceramic-rich surface to a

metal-rich surface, with desired variation of the volume fractions of the two materials in

between the two surfaces. Functionally Graded Material (FGM) belongs to a class of

advanced material characterized by variation in properties as the dimension varies. The

overall properties of FMG are unique and different from any of the individual material that

forms it. There is a wide range of applications for FGM and it is expected to increase as the

cost of material processing and fabrication processes are reduced by improving these

processes. In this study, an overview of fabrication processes, area of application, some recent

research studies and the need to focus more research effort on improving the most promising

FGM fabrication method (solid freeform SFF) is presented. Improving the performance of

SFF processes and extensive studies on material characterization on components produced

will go a long way in bringing down the manufacturing cost of FGM and increase

productivity in this regard.

GRADING % OF METAL + GRADING % OF CERAMIC = FGM MATERIAL

For example, thermal barrier plate structures for high-temperature applications may form

from a mixture of ceramic and a metal. Primarily meant for high temperature applications in

space shuttle, rockets, etc..

2. LITERATURE SURVEY

Normally, a component can be fabricated using any metal. However, for some specific

applications such as in aerospace engineering where the component’s weight and durability in

high temperature environment are so crucial, the components need to be fabricated using

special material such as a functionally graded material (FGM). Pure metals are of little use in

engineering applications because of the demand of conflicting property requirement. A

comprehensive shear deformation theory in combination with isogeometric method for

momentary analysis of functionally graded material (FGM) plates. diffferent examples are

obtainable to explain the effectiveness of the proposed method [1]. The purpose of an well-

organized beam theory for bending, free vibration and buckling analysis FGM. This analysis

considers for both shear deformation and thickness stretching possessions. It can be

completed that, this analysis is accurate for all type analysis for FGM [2]. Buckling analysis is

used to analysis the FGM by nonlocal third-order shear deformation method [3]. A cylindrical

FGM shell model is developed for analysisng by nonlocal strain gradient theory. The result

shows that the developed model are evaluated with the Eringen’s nonlocal, strain gradient,

modified couple stress and classical theories. The conclusion of the evaluation is that the

nonlocal strain gradient is outperformed the other methods [4]. Nonlinear dynamic response

of higher order shear deformable FGM circular cylindrical shells subjected to thermo-electro-

mechanical and damping loads. Numerical results show the influence of geometrical

parameters, material properties, imperfection, elastic foundations, and thermo-electro-

mechanical and damping loads on the nonlinear dynamic response of the shells [5]. An

efficient and simple sophisticated shear deformation theory is offered for the vibration and

buckling of exponentially FGM sandwich plate under various boundary conditions. The

accuracy of the proposed theory is confirmed by comparing the obtained results with

solutions available in the literature. Numerical results show that the present theory can archive

accuracy comparable to the existing higher order shear deformation theories that contain more

number of unknowns [6]. The free vibration analysis of FGM beam made of porous material

by the semi-analytical differential transform method. Exhaustive mathematical equation are

proposed and numerical examination are performed [7]. Flexural vibration analysis of beams

is developed by FGM with various boundary conditions. The customized rule of mixture is

utilized to analyze the material properties of the FGM beams. Based on numerical results, it is

Design and Analysis of Functionally Graded Cylindrical Shell by Applying Static and Buckling Load


exposed that FGM beams with even distribution of porosities have more significant impact on

natural frequencies than FGM beams with uneven porosity distribution [8].

The free vibration behavior of FGM plate is examined under prominent thermal

environment. The strength and the union behavior of the present numerical results have been

compared with previous result from literature. The result shows that the developed approach

is one of the best methods to analyze the FGM [9]. The Euler–Bernoulli model with the

consistent size-dependent theory, the nonlinear formulation of functionally graded

piezoelectric material nano beam is developed. The effects of electrical force, mechanical

force, and material properties of functionally graded piezoelectric material beam on the static

responses, buckling, and free vibrations are discussed and some significant results are

obtained [10,11]. The vibration and dynamic instability of cylindrical shells made of FGM

and containing flowing fluid are studied. It is demonstrated that by increasing the value of

material property gradient index of FGM, the natural frequency of the first mode and the

critical flow velocity of the system increase [12]. In this study, the static (Deflection) of FGM

cylindrical shell, static (circumferential stress, longitudinal stress), Eigen buckling analysis

(critical load), modal analysis by finite element analysis ANSYS software under mechanical

load for different end conditions are studied.

3. PROBLEM DEFINITION

In composites the interface problems occurs due to the changes in material properties and

orientation across the cross sections leading to delamination. FGM materials are the

continuous change in their mechanical and thermal properties. The mechanical properties

changes gradually in the thickness direction according to the volume fraction by power law

distribution. Analyzing a FGM cylindrical shell analytically and numerically using ANSYS

package under both the compressive force leads to buckling and vibrations of component is

considered in this work. This study is used to investigate the FGM Fuel tank for launchers

(thin cylindrical shell which is made up of stainless steel and Alumina) and FGM under

compressive loads.

In this study, the static (Deflection) of FGM cylindrical shell, static (circumferential

stress, longitudinal stress), Eigen buckling analysis (critical load), modal analysis by finite

element analysis ANSYS software under mechanical load for different end conditions is

studied. The objectives of the proposed study,

To develop the model in ANSYS 15.0 for simulation and validating results with reference

journal for isotropic cylinder under mechanical load.

To develop the model in ANSYS 15.0 and evaluate the material properties of FGM

cylinder along the thickness direction.

To conduct structural analysis (circumferential stress, longitudinal stress) in ANSYS

under compressive load.

To conduct Eigen buckling analysis (to find critical load).

To carry out modal analysis under free vibration (mode shape & natural frequency).

3.1. Pressurized Thin Walled Cylinder Shell

Pressure vessels are exceedingly important in industry. Normally two types of pressure vessel

are used in common practice such as cylindrical pressure vessel and spherical pressure vessel.

In the analysis of this walled cylinders subjected to internal pressures it is assumed that the

radial plans remains radial and the wall. Further in the analysis of them walled cylinders, the

weight of the fluid is considered negligible. Let us consider a long cylinder of circular cross –

section with an internal radius of R 2 and a constant wall thickness as showing fig.



Figure 3.1 cylinder of circular cross – section

This cylinder is subjected to a difference of hydrostatic pressure of ‘p' between its inner

and outer surfaces. In many cases, ‘p' between gage pressure within the cylinder, taking

outside pressure to be ambient. By thin walled cylinder we mean that the thickness t is very

much smaller than the radius Ri and we may quantify this by stating than the ratio t / Ri of

thickness of radius should be less than 0.1.

An appropriate co-ordinate system to be used to describe such a system is the cylindrical

polar one r, q, z shown, where z axis lies along the axis of the cylinder, r is radial to it and q is

the angular co-ordinate about the axis. The small piece of the cylinder wall is shown in

isolation, and stresses in respective direction have also been shown.

3.2. Failure of Thin Cylindrical Shell

Such a component fails in since when subjected to an excessively high internal pressure.

While it might fail by bursting along a path following the circumference of the cylinder.

Under normal circumstance it fails by circumstances it fails by bursting along a path parallel

to the axis. This suggests that the hoop stress is significantly higher than the axial stress. In

order to analyze the thin walled cylinders, let us make the following assumptions:

• There are no shear stresses acting in the wall.

• The longitudinal and hoop stresses do not vary through the wall.

• Radial stresses sr which acts normal to the curved plane of the isolated element are negligible

small as compared to other two stresses especially when [t/R < 1/20]

The state of tress for an element of a thin walled pressure vessel is considered to be

biaxial, although the internal pressure acting normal to the wall causes a local compressive

stress equal to the internal pressure, Actually a state of tri-axial stress exists on the inside of

the vessel. However, for the walled pressure vessel the third stress is much smaller than the

other two stresses and for this reason in can be neglected. When a thin – walled cylinder is

subjected to internal pressure, three mutually perpendicular principal stresses will be set up in

the cylinder materials, namely, Circumferential or hoop stress and longitudinal stress.

4. FINITE ELEMENT ANALYSIS OF FGM CYLINDRICAL SHELL

Thin cylindrical shell is made by FGM. In this FGM, The stainless steel is used as a metal and

aluminum oxide (alumina) is used as a ceramic. Because, the stainless steel is having high

wear-resistant, low coefficient of thermal expansion, good thermal conductivity, excellent size

&shape capability, High strength and stiffness and the aluminum oxide excellent corrosion

resistance, good formability, excellent physical properties, less price high competitiveness and

good stability. The matrial properties are listed in Table.1.



Table 4.1 Material properties

Materials

Young’s

modulus

(GPa)

Poisson ratio

Density

(kg/m3)

Thermal

Conductivity

(W/mK)

Thermal

Expansion

(X 10 -6

/ K)

Alumina 380 0.3 3800 10.4 7.4

Stainless

steel

210 0.3 7850 24 16.8

4.1. Finite Element Modelling and Meshing

4.1.1 Modeling

The 3-D model of functionally graded material plate of size 1 x 1 m for finite element analysis

is generated. According to the concept for functionally graded plate shell 181 is used. Shell

181 structural elements give the layer by layer generation to form FGM beam according to

our necessity. The following figure shows the layer formation of FGM beam.

Figure 4.2 Layer formation for 20 layer FGM cylindrical shell

4.1.2. Meshing

For the shell model mesh will be an important role for analyzing. We have to converge the

result by varying the mesh size, so that the results will be accurate for the simulation model to

perform further analysis by providing the boundary condition and apply load.

4.2. Power Law Index

The power law distribution in thickness direction considered is given by the following

equation. In each layer, the material property which is a function of thickness is given by the

distribution equation.



1. Material properties are dependent on the k value and the position and vary according to a

power law.

2. When k = 0 the plate is a fully ceramic plate while at k = 8 the plate is fully metal.

E (Z) = (Ec – Em) V + Em

Where Ec & Em are the young’s modulus of the ceramic and young’s modulus of the

metal; k is the parameter that dictates the material variation profile through the thickness.

Figure 4.3 Variation of Young Modulus through the Thickness of Alumina/Aluminium FGM Plate

4.3. Static Analysis in Cylindrical Shell

The bending behavior of alumina/aluminum cylindrical shell under distributed transverse load

is load is taken up for investigation. The top surface of the cylinder is ceramic (alumina, Ec =

380 GPA, Vc =0.3) rich and the bottom surface is metal (aluminum, Em = 70 GPA, Vm =0.3)

rich. The variation of the volume-fraction of ceramic Vc and the effective young’s modulus E

in the thickness direction Z=h/2 of a functionally graded cylinder is obtained by rule of

mixtures. To start with, the efficacy of the present formulation is assessed by studying a

simple supported thin ( a/h = 100) isotropic cylindrical shell under uniformly distributed

load. The non-dimensional central displacement, maximum bending moment and maximum

shear force obtained here are compared along with the analytical solution and they match very

well.

5. STRESS ANALYSIS

5.1. Stress Analysis of FGM Cylindrical Shell

This section describes the steps of simulation of FGM cylindrical she by using ANSYS

software. It includes finite element mesh selection of suitable elements and descriptions of

element used are presented in respectively. Modeling the boundary conditions and loads are

given and adjusting the options to solve properly is described. The steps are described in

detail in the proceeding section it shows in Fig. 5.1.



Figure 5.1 Cross sectional view of cylinder

Description of cylinder Number of layers = 20

Outer diameter = 57 mm

Inner diameter = 54 mm

Height = 171 mm

Thickness = 3 mm

5.1.1. Element selection

The present case is a structural, modal and harmonic analysis of FGM cylindrical shell. The

number of layer and properties are varying along the thickness direction. The property varies

for each layer. So, the SHELL 81 for this analysis. Shell is mostly used for building one layer

over other.

5.1.2. Boundary Conditions and Loads

Cylindrical shells are mostly used to storage tanks. The pressure acts on the internal wall of

the cylinder and causes the deflection. The basis of simulation has been carried out by using

ANSYS finite element package.

5.1.3. Stress Assumptions

Cut the cylinder by two normal planes at x and x + dx, and then by two planes θ and θ + dθ as

shown in Figure 5.2,5.3 and 5.4. The resulting material element, shown in exploded view in

Figure has six surfaces. The outer surface r = R is stress free. Thus srr= trx= trθ=0 at r = R.

Figure 5.2 Wall material element of a pressurized cylindrical vessel referred to Cylindrical

coordinates.



On the inner surface r = R -t there is a compressive normal stress that balances the applied

pressure but no tangential stresses. Thus srr= -p, trx= trθ=0 at r = R -t Since the wall is thin,

we can confidently assume that trx= trθ= 0 for all r ∈[R -t, R] whereas srr varies from -p to

zero. Later on we will find that srr is much smaller than the other two normal stresses, and in

fact may be neglected we conclude that tzr= tθr= 0 for all r inside wall. The normal stresses

sxx and szz are called axial stress and circumferential or hoop stress, respectively.

The last wall stress component is tθx = txθ, which is the wall shear stress. Because of

symmetry assumptions on the geometry and loading stress is zero. These stress assumptions

are graphically displayed, with annotations, in Figure Displaying the wall stress state using

the stress matrix and taking the axes in order {x, θ, and r} for convenience, we have

Comparing this to the 2D stress state introduced in Lecture 1, we observe that the cylinder

vessel wall is in plane stress.

Figure 5.3 Free body diagrams (FBD) to get the averaged hoop and longitudinal wall stresses in a

pressurized thin-wall cylindrical vessel

Figure 5.4 Cylindrical vessel wall

5.1.4. Isotropic Cylindrical Shell Analytical Calculations

First step is to analyze the stress distribution in the cylinder and find out the circumferential

stress and longitudinal stress present over the ceramic phase to metal phase. As we know that

cylindrical shell formulas are Circumferential stress = ( p X d) / 2t and Longitudinal stress = (

p X d) / 4t.



Where, P = internal pressure in N/m2; d = diameter in m; t = thickness in m

The value of pressure, diameter and thickness are taken as,P = 5000 N/m2, d = 0.6 m, t =

0.005 m;

Theoretical calculation:

Longitudinal stress = ( p X d) / 2t = (5000 X 0.6) / 2 X 0.005 = 150000N/m2

Circumferential stress = ( p X d) / 4t = (5000 X 0.6) / 2 X 0.005 = 75000N/m2.

Analtical calculation result as follows, Longitudinal stress = 150000N/m2 and Circumferential

stress = 75000N/m2. This result conform that the developed thin cylindrical shell is in good

design model. Developed FGM cylindrical shell is shown in fig. 5.5.

Figure 5.5 FULL MODEL FGM CYLINDRICAL SHELL

5.1.5. Steps Involved in Stress Analysis of Cylindrical Shell

In fig 5.6 For easy analysis purpose we have taken quarter portion of thin cylindrical shell.

This will also saves more time for analysis. Fig 5.7 shows the meshed selected quarter portion

of thin cylindrical shell. We have divided the total length into 50 equal parts and diameter is

divided into 20 equal parts. Fig 5.8 is defined the boundary conditions. The bottom surface of

thin cylindrical shell is fixed. The sides of thin cylindrical shell are symmetric in dimension.

Fig 5.9 shows the result of stress analysis for applied boundary conditions k=0 are obtained.

The red region in the shell indicates the high stress and blue region indicates the less stress

region in the thin cylindrical shell.

Figure 5.6 F.E.Model Figure 5.7 Meshing



Figure 5.8.Boundary Conditions Figure 5.9. Longitudinal Stress

Figure 5.10 Figure.5.11

Figure .5.12 Figure.5.13

Figure.5.14 Figure.5.15





Fig 5.10-5.19 The results of stress analysis for applied boundary conditions and material

composition k=0.2,3,4,5,10,20,30,50,70,80 &100 are obtained.

TABLE 5.1 Results of longitudinal stress and circumferential stress at specific material composition

(k)

Material composition Longitudinal Stress (N/m2) Circumferential Stress

(N/m2)

K=0 74334 148668

K=0 .2 75163 150326

K=3 75267 150534

K=3.3 76049 152098

K=4 77424 154848

K=5 78973 157946

K=10 83132 166264

K=20 86156 172312

K=50 87733 175466

K=70 83263 166526

K=80 81165 162330

K=100 74334 148668

The results for longitudinal stress and circumferential stress for various material

composition obtained from numerical method analysis in ANSYS and listed in Table 5.1.



5.2. Buckling of FGM Cylindrical Shell

Buckling is a critical phenomenon in structural failure. Buckling is the failure of structures

under compression load. Also buckling strength of structures depends on many parameters

like supports, linear materials, composite or nonlinear material etc. When a structure

subjected usually to compression undergoes visibly large displacements transverse to the load

then it is said to buckle. Buckling may be demonstrated by pressing the opposite edges of a

flat sheet towards one another. For small loads the process is elastic since buckling

displacements disappear when the load is removed. Local buckling of cylinder or shells is

indicated by the growth of bulges, waves or ripples, and is commonly encountered in the

component cylinder of thin structural members. The effect of thickness on buckling load and

stresses are plotted. The buckling load is increasing with increase in thickness.

5.2.1. Types of Elements

5.2.1.1. Plates

Element whose geometry lies in the plane with loads acting out of the plane which cause

flexural bending and with both in plane dimensions large in comparison to its thickness - two

dimensional state of stress exists similar to plane stress except that there is a variation of

tension to compression through the thickness.

5.2.1.2. Shells

Element similar in character to a plate but typically used on curved surface and supports both

in Plane and out of planeloads – numerous formulations exist.

Figure 5.20 F.E. Model Figure.5.21 Boundary conditions

5.2.2. Buckling of thin-walled structures

A thin-walled structure is made from a material whose thickness is much less than other

structural dimensions. Into this category fall plate assemblies, common hot- and cold- formed

structural sections, tubes and cylinders, and many bridge and aero plane structures.

5.2.2.1. Boundary conditions

The quadratic model is considered for the analyzed, the line 1 & 2 is symmetrical boundary

conditions, and the bottom end is fully arrested for the translation and rotational. The top

surface is loaded by the unit load. To find critical load the Eigen solver must be provided with



the unit load conditions. If we apply other than one takes the scale ratio with the obtained

result. Thus from this analysis it is found that load carrying capacity is high for the ceramic

and gradually decreases towards the metallic phase. The critical buckling load is high for

ceramic and gradually low towards the metal. Buckling load directly depends on the material

composition and position of the measured variable. The buckling result are shown the

following Table 5.2

Table 5.2 Result of Buckling at specific material composition

Material composition (k) Critical Load

K=0 0.143+E8

K=0 .2 0.132+E8

K=3 0.998+E7

K=3.3 0.987+E7

K=4 0.969+E7

K=5 0.949+E7

K=10 0.892+E7

K=20 0.847+E7

K=50 0.809+E7

K=70 0.800+E7

K=80 0.797+E7

K=100 0.788+E7

Thus from buckling analysis the critical loads are obtained for the different material

compositions. Load carrying capacity is high at ceramic layer and it gradually decreases

towards metal layer due to their stiffness properties. stress is studied in this work. First, the

FG cylindrical shell is assumed to be isotropic (Ceramic rich) and the ANSYS results are

validated with the analytical results are discussed. Then the buckling analysis is carried out to

find critical load.

6. RESULTS AND DISCUSSION

From the Table 5.1., the different material composition is chosen for finding the hoop and

longitudinal stress. Upto k = 4, there is no that much difference in the stresses values. It is

equal to the theoretically calculated value. When the ‘k’ value further increases the stress

values are crossed that theoretical value. So that, up to that material composition (k = 4), the

FGM cylindrical shell is not failed. In the Table 5.2, the calculated critical load values for the

same material composition are tabulated. From the result, the critical load is increased upto k

= 5 and it is decreased. It confirmed that the critical load is depends upon the material

combosition.

7. CONCLUSION

The finite element analysis method static analysis of cylindrical shell made of Functionally

Graded Materials (FGM). The static analysis of a functionally graded plate and cylinder of

variable thickness under mechanical load, stress is studied in this work.

From static analysis of thin & thick plate, the deformation is low at ceramic phase and

increases gradually towards the metallic phase, “ceramic resist deformation, metal has high

deformation”.

From static analysis of cylinder, the circumferential stress & longitudinal stress decreases

gradually from ceramic phase towards the metallic phase, “because stiffness is high for



ceramic, low for metal”. For Numerical approach 10%-15% of error is accepted but in our

case it’s lesser than 1%, hence we produce results at greater accuracy.

From buckling analysis of cylinder, the critical load decreases gradually from ceramic

phase towards the metallic phase. Load carrying capacity depends on position and

composition of ceramic and metallic constituents.

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DESIGN AND ANALYSIS OF FUNCTIONALLY GRADED … · Keyword: Functional Graded Material Analysis, Buckling Analysis Cite this Article: M. Shunmugasundaram, D.Maneiah and CH.Nagaraju,