Fem Questionpapers

7/21/2019 Fem Questionpapers

1/33

Tirne:

3 hrs.

USN

c.

2a.

b.

c.

3a.

b.

c.

4a.

b.

06ME63

(08

Marks)

(04

Marks)

(10

Marks)

(05

Marhs)

Sixth

Semester

B.E. f)egree

Examination,

December

2Ol2

Modeling

and

Finite

Element

Analysis

.

a

u

e

=

a

O

aX,

=D-

3

otll

=co

.= a.l

Etf

-O

=ts

a2

6=

OO

-1

boi

2G

3u

AE

6X

o

--:

,i

.9.

6E

oLE

a,-

>(k

cno

=

bIr

0=

soF>

o

(-)

.9

on-

troo

qo

:a)

EE

-h

c'i

o

o

d

o

o,

b.

c.

of

the

spring

system

shown

principle

of

minimum

potential

en?rg{;

t{"

trln"*

Sorf

Fig.Q.1(c).

6-s

rr

lx't

Explain

the

discreti

zationprocess

of

a

given domain

based

on

element

shapes

number

and

(06

Marks)

slze.

Explain

basic

steps

involved

in

FEM

with

the

heip

of

an example

involving

a structural

member

subjected

to

axial

loads.

(08

Marks)

Why

FEA

is

widely

accepted

in

engineering?

List

various

appiications

of

FEA

in

engineering

(06

Marks)

Derive

interpolation

model

for

2-D

simplex

element

in

global co

-

ordinate

system'

(10

Marks)

What

is an

interpolation

function?

Write

the

interpolation

functions

for:

i)

1

-Dlinearelement

;

ii)

1

-Dquadraticelement'

iiU

2-D

linearelement

;

iv)

2-Dquadraticelement'

v)

3-Dlinearelement.

Explain

"complete"

and "conforming"

elements'

Derive

shape

function

for

1

-

D

quadratic

bar

element

in

neutral

co-ordinate

tVttelm

Marks)

Derive

shape

functions

for

CST

element

in

NCS.

(08

Marks)

What

ur.

rhup.

functions

and

write

their

properties.

(any

two).

(04

Marks)

(06

Marks)

(04

Marks)

(04

Marks)

(06

Marks)

(10

Marks)

c.

4a.

5a.

b.

c.

6a,

b.

PART

-

B

Derive

the

body

force

load

vector

for I

-

D

linear

bar

etrement.

Derive

the Jacobian

matrix

for

CST

element

starting

from

shape

function'

Derive

stiffness

matrix

for

a

beam

element

starting

from

shape

function'

Explain

the

various

boundary

conditions

in steady

state

heat

transfer

problems

with

simple

sketches.

(06

Marks)

Derive

stiffness

matrix

for

1

-

D

heat

conduction

problem using

either

functional

approach

(08

Marks)

or

Galerkin's

approach

I

of

Z

Srtcll.t"r


4/33

06M863

(06Marts)

Take

Ar:Az=A3:A

Fie.Q.6(c)

7

a.

The

structured member

shown

in

figure

consists

of

two

bars.

An

axial

load of

P:200

kN

is

loaded

as

shown.

Determine

the

following

:

i)

Element stiffness

matricies.

ii) Global

stiffness

matrix.

iii)

Global

load

vector.

iv)

Nodaldisplacements.

c.

For the

composite

wall

shown

in the

figure,

derive

the

global

stifftress

matrix.

fo;5s1.

Fs

z

rD

qlt

.t-tot$fltt

Fie.Q.8(b)

,*****

2

of?

i)

Steel

Ar

=

1000

mm2

Er

:200

GPa

ii)

Bronze

Az:2000

mm2

Ez:

83 GPa'

8

a. Determine

the temperature

distribution

in

1

-

D

rectangular

cross

-

section

figure.

Assume that

convection

heat loss

occurs

from

the end of

the

fin.

Take

-

0.1w

h

=

""

=

,

T*:20oC.

Consider

two elements

Cm'oC

fo

v 5

E*fr.,r

Fr

z

reg,il

.f.y-tol

nnll

Fie.Q.8(a)

b.

For the cantilever

beam subjected

to

UDL

as

shown

in Fig.Q.8(b),

determine

the

deflections

(08

Marls)

b.

For

the truss system

shown,

determine

the

nodal displacements.

Assume

E:

210 GPa

and A

= 500 mm2 for both

elements.

(I2

Marks)

;f

=loovl.rt

fin

as shown

in

'3w

=-.

CmoC'

(10

Marks)

Fie.Q.7(b)

of

the

free end.

Consider

one

element.

(10

Marks)


5/33

USN

Time:3

hrs.

SixthSemesterB.E.DegreeExamination,December2010

Modeling

and

Finite

Element

Analysis

06ME63

Max.

Marks:100

Note:

Answer

ony

FIVE

futl

questions'

selecting

at

least

TWO

questions

from

each

part'

PART

_

A

I

a.

Explain,

with

a

sketch,

plain

stress

ffi'"-"

tt

"in

for

two

dimensions'

(06

Marks)

b.

State

the

principles

of

minimu*

p*"'ii"f

energy'

Explain

the

potential

energy'

with

usual

(06

Marks)

o

,9

H

a

(g

d

()

d

0)

39

d9

-o

,,

ao"

Fm

.=+

'E-f

b?p

Pfr

o>

1

a

acd

5(J

do

6d

}E

tr5

O

oe

o-

gt

Eo.

si

^9

'@q

L0

>.k

mo

=(6

0

tr>

59

o-

U1

7.

+v

Qg

@

t

3otv\

t"t

I

(5x&20

Marks)


23/33

Poge

No.,.

I

ME6FI

Reg.

No.

2*t+3a2*nJ:-1

541*e2*rs:0

3rr

+

2a2l4a3

-']".1

2.

@,

(b)

(c)

3.

tol

potentiol

energy

of o

solid bor

under

compression.

(c)

Exploin

the

Royleigh-Ritz

method

with

on exompte.

Sixth

Semesler

B.E.

Degree

Exominolion,

Jonuory/Februory

2006

Mechonicol

Engineeilng

(Old Scheme)

Finiie

Elemenl

Methods

'1.

Time:

3 hrs.)

':.

NOle:

Answer

ony FIVE

tuil

queslions.

I.

(o)

Find

the

inverse

of

[r ol

lo

rl

,o,

a:

[3

1]

,:l;

{l

Find

:

i)

AB

ii1

BT ar

(c)

Solve

by

Gouss

eliminotion

4.

(o)

Exploin

the

Golerkin's

opprooch

for

obtoining

stiffness

motrix

of

o

bor

element,

(10

Morks)

(b)

TwopointsPl(10,8)ondP2(80,10)onosotidbodydisptocesto pl(Lo.z,b.4)ond

Pj(80.5,10.2)

ofter

looding.

Determine

normol

ond

sheor

stroins,

(t0

Mql1s)

Confd....

2

Whot

is

finite

element

method?

Whot

ore

the

odvontoges

of FEM

over finite

difference

method?

(4

Morks)

Exploin

boundory

volue ond

initiol

volue

problems

using

suitoble

exomples.

'

(8

Morks)

Exploin

the

steps

involved

in

the

finite

element

onolysis

of

solids

ond

structures.

:

.

(S

Morks)

whot

is

meont

by

'Bcind

width'

of

o

motrix?

Give

on

exomple,

Exploin

why

it

should

be minimized,

(6

Morks)

(b)

Stote

the

principle

of minimum

potentiol

energy,

ond

derive

on expression

for

totol

(Mox.Morks:

100

(5

Morks)

(5

Morks)

(10

Morks)

(6

Morks)

(8

Morks)


24/33

Poge

No,,, 2

5. A solid stepped bor

os

shown in

fig.l

is

subjected to

on oxiol force.

following

i) Element

ond ossembled

stiffness

motrix

iD Displocement of eoch''node

I

iii)

Reoction force

of

fixed

end

ME6FI

Determine

the

(20

Morks)

2-

A,=

tOo

hm

,

*r=LOo

mhn-

g

=

2,00G

Pa

rt"=

lo

q

Pq

h-k

u

6.

(o)

Whot is

Jocobion

Motrix? Derive o

Jocobion

motrix

for

Two-Dimensionol

element.

7.

@|

Derive

shope functions

for o

l-D

quodrotic

element with

3 nodes.

(t0

Morks)

(b)

Exploin

convergence

criterio ond

potch

test in

brief.

(10

Morks)

(b)

Derive

shope function

CST

triongulor

element,

8.

Write

short note

on ony

FOUR:

o)

Voriotionol

opprooch

6)

'Hermition

shope functions

c)

Penolty

opprooch

for hondling

boundory conditions

d) Logronge

ond

serendipity fomily

of

elements

e)

ISO

porometric

elements

(10

Morks)

(10

Morks)

(5x4

Mqrks)


25/33

Page

No..,

1

USN

ME6Fl

1.

[Max.Marks

:

10O

(10 Marks)

(5

Marks)

3.

4.

(b)

Explain

the

criteria

for

monotonic

convergence.

(,l0

Marks)

5.

(a)

A component

shown

in fig.

5(a)

is

subjected

to

a

load

5 kN.

Determine

the

foilowoing.

i)

Element

stiffness

matrices

ii)

B

-

matrices

iii)

Displaeements

and

strains

iv)

Stresses

and

reactions.

Obtain

the

stiffness

matrix

and load

vector

assurning

two

eiements.

(b)

What

are

characteristics

of stiffness

matrix

?

$ixth

sernester

B"E.

Degree

Examination,

July/August

2004

Mechanical

Engineering

Finite Element

Methods

3 hrs.l

Note:

1. Answer

any

F|VE

full

questions.

2. Assume

suitable

data if

necessary.

(a)

Explain

with

example,

i)

Syrnmetric

matarix

ii)

Determinant

of a

matrix

iii)

Pcsitive

definite

matrix

iv)

Half band

width

v)

Partitioning

of

matrices.

(b)

Give the

algorithm

for

forurard

elimination

and

back

substitution

of

Gauss

elimination

for

a

general

matrix.

(io

Marks)

2.

(a)

With

suitable

examples

explain.

i)

Essential

(geometric)

boundary

mndition

ii)

Ndtural

(force)

boundary

condition.

(b)

outline

the

steps

in finite

element

analysis.

(5

Marks)

(c)

State

the

principle

of

minimum

potential

energy.

Obtain

the

equilibrium

equation

ol the

system

shown in

fig 2.c

using

the

principle

of-minimum potentidl

energy. (10

Marks)

(a)

Derive

the

equilibriqm equation

ol

3D.elastic body

oc.cypyt"ng

a

volume

V

and

having

a

surface

s, subjected

to

body

force and

a

concentrated

lddd.

(r0

Marks)

(b)

ry

elastic

bar

of length.L,

modulus

of

elasticity

E, area

of

cross

section

A, which

is

fixed

at

one

end and

is

subjected

to

axial load

at-the

other

end.

Obtain

the'Euler

equation

governing

the

bar,

and

natural

boundary

conditions.

t10

Marks)

(a)

Fo1

a two

noded

one

dimensional

element,

show

that

the

strain

and

stress

are

constant

with

in

the

element"

(ro

Marks)

('t2

Marks)

(8

Marks)

(a)

For

a.pin

jointed

configuration

shown

in

Fig

6.a

detennine

the stiffness

matrix.

Also

determine

qt

interms

of g,.

(10

Marks)

(b)

Derive

the

Hermite

shape

functions

of

a

beam.

(10

Marks)

Contd....

2


26/33

Page Nor,

2

7.

(a)

Evaluate

illE6F1

(5

Marks)

{b)

Derive

the

expression for

shape

lunctions

of eight

noded

isoparametric

element.

(15

Marks)

1

-1

Using

two point

Gauss quadrature.

8.

(a)

(b)

Determine

the

Jacobian for

the triangular

element

shown

in fig

eg.a,

(5

Marks)

Give

thp

element

number and

mode

numbers

for

the

structure

shown in

Fig

Q

8.b, so

as

to minimize

the half

band

width

of the resulting

stiffness

matrix.

(5

Marks)

(c)

For

the beam

shown in fig

Q.8c.

obtain the

global

stiffness

matrix.

(10

Marks)

fi?.

qL.

e-

vf,

ct'o'+c>

)

t o',

-/"

Et

7oxto3^l/t''ol

I {/

A=

l3oo

ss

m"n'

I

J.

Clo,rs)

V--

S

n

t

fr3.

Q6.a

)',\+;')

,

/ \

C z

s's)

L1.51)

63'

Qe'o-

+R

s

t.

q8.

b

A.;

5oo

mm

,

gn:

QOO

mw

c :

\0o

GPa'

L';

r-oo

aOo.

F3

5(a1

h-

I'ro

nD

I

.tlo

-,

,@

/l

^^

,-2oo\ld.

.qc.c

i=

"^lo6+nYo*

\t

*****

le

\ooo

,


27/33

Page No... 1

USN

ME6F1

Time:

3

hrs.l

Note:

Sixth Semester B.E. Degree

Examination,

January/February

2004

Mechanical

Engineering

Finite

Element

Methods

1.

Answer any FIVE

full

questions.

2. Missing data

may

be

suitably

assumed,

1.

(a)

Find the eigen values of

A-

4

-{51

-,/3

a

l

(5

Marks)

(b)

Solve

the following

system of simultaneous equations

by

Gaussian elimination method.

2e1*12 3rs:t$

4r1*r21.a3:$

3n1*2r2

*

rs:3

(c)

Define

the

following

with

example

i)

Skew

matrix

ii)

Symmetric

banded

matrix.

(a)

Explain

difference

between continuum method

and finite

element method,

(5

Marks)

(b)

Explain

basic steps involved in FEM.

(10

Marks)

(c)

Explain

principle

of

minimum

potential

energy and virlual

work.

(5

Marks)

(a)

Expain

steps involved

in

Rayleigh

-

Ritz

method.

(B

Marks)

(b)

Determine

the deflection at the free

end of

a

cantilever

beam

of length

'1,

carrying

a

vertical

load

'P'

at its free end

by

Rayleigh

Ritz

method (i0

Marks)

List the demerits of cantinuum

methods.

(2

Marks)

Derive

strain

displacement

matrix,

stiffness

matrix for

one

dimentional bar

element.

(8

Marks)

Solve for stresses

and strains for

the following

problem

by using

bar element.

(12

Marks)

?

=

loco

l.J

/t


28/33

Page

N0...

5.

(a)

(b)

2

Derive

stiffness

matrix

for

a

truss

element.

Ar

:

LAA\mmz

Az:125Amm,2

E:200GPa

ME6F1

(8

Marks)

(12

Marks)

(16

Marks)

(4

Marks)

using

one

triangular

(20

Marks)

For

a

pin

jointed

configuration

shown

in

figure,

determine

nodal

displacements

and

stress

by

using

truss

elemenls.

f

:

looo;?

T

5oo

r

t

6.

(a)

Compute.the

deflection

of simply

supported

beam

carrying

concentrated

load

at its

centre,

Use

two

beam elments.

:lSovnr'

(b)

ls

FEM

analysis

applicable

for

highly

elastic

materials?

Explain.

Find

the displacement

of

node

1 in

the

triangurar

element

shown

element.

Also

find

stress

and

strain

in

the

elefient.

7.

loo

l,/

I.(,2,o

)

5o

I

E:70GPa

L

7:0.3

Le

:

lAmm

3o,

Write

short

notes

on

any

FOUR

of

the following

:

a)

Static

condensation

b) lsoparametric,

super

parametric

and

subparametrlc

element

c)

Static

and

kinematic

boundary

condition

d)

Lagrangian

and

Hermite

shape

functions

e)

Convergencecriterion

*****

.

1+-----

3o

n

(-3o,o

)

\l

r.-__

I

2o

(4x5=2Q

fYl2Y[s)


29/33

-----

'

Page

N0,,. I

USN

ME6F1

[Max.Marks

:

10O

(10

Marks)

(5

Marks)

(5

Marks)

(10

Marks)

(4

Marks)

(6

Marks)

(10

Marks)

Use

penality

(10

Marks)

.,

r

2lo$ pa

?JaoN

(10

Marks)

Sixth

Semester B.E.

Degree

Examination,

July/August

2000

Mechanical

Engineering

Finite

Element

Methods

Time:

3 hrs.I

Note: Answer

any

FIVE

futt

questions.

1.

(a)

Given

o:l;

i],

ort.,*in.

i)

Inverse

of

matrix

ii)

Eigen

values.

(b)

lf

,7"r:

[,

1-(2],

evaluate

/,

wT Nag

(c)

Explain symmetric

banded matrix.

2.

(a)

With

an

example explain Rayleigh

-Ritz

method.

(b)

State the

principle

of

minimum

potential

energy.

(c)

Sketch the

quadratic

and Hermite

shape functions.

3.

(a)

Derive

the following

characteristics

of three noded

l-D

element.

i)

Strain displacement matrix

[B]

ii)

Stiffness matrix

[frr]

4.

(a)

Derive

an

expression for

i)

Jacobian matrix

ii)

Stiffness matrix

for axisymmetric

element.

(b)

Solve for nodal

displacements and

stresses for

the structure

shown in

fig

1.

approach

to apply

boundary csnditions.

h

t"laao

n{'

2"17o

frrn*

*1,=zo$fo"

Contd....

2


30/33

_

Page

N0...

2

(b)

0onsider

a

rectangular

element

as

shown

in

Fig.2.

Evaluate

(=0,

\=0,

ME6F1

J and B matrices

at

(10

Markr)

+

t

A,>

-t

a)

(0,

,)

5.

(a)

Explain

with neat

sketches

the

library

of elements

used

in FEM.

(10

Marks)

(b)

Using

Gaussian

quadrature, evaluate

the

following

integral by two

point

formula

d, /],

(2

+

zrt

+ rf)

dt

drt

(10 Marks)

6,

(a)

For

the

pin

jointed_

configuration

shown

in Fig.3

determine

the stiflness

values

of

' '

kn,

l*e

and,-k2,

of

global stiffness

matrix.

(10

Marks)

O

hra'tgroivl"nL'

L

"l/

b

MvY'

E-

>}lac\?",

,

(b)

Derive

an expression

lor

stiffness

matrix

ol

a

two noded beam

element.

(10

Marks)

7.

(a)

Explain in detail the leatures

of

any one commercial

FEA

software

package.

(l0Marks)

(b)

Bring

out

the

differences

between

continuum

methods and

FEM.

(10

Marks)

Write short

notes on

any

FOUR

:

a) State

functions

b) Galerkin

methods

c)

Elimination

method

of handling

boundary

conditions.

d) Temperature

effects

e) Convergence

criteria.

**

*

**

/L

I

I

vjup

l\n7

+

C1i,o,{)

cv>-

(4x5=20

Marks)


31/33

Page

No...

l

ME6Fl

Reg.

No.

sixth

serrester

B.E.

Degree Examflnatlon,

Februar5r

zooz

Mechanical Englneering

Ftntte

Element

Methods

Time:

3

hrs.l

[Max.Marks

:

I0O

Note:

Answer any

FIVE

full

questions,

1.

(a)

What

is

a banded

matrix

and

state

its

advantage?

(b)

Calculate

the

eigen

values

of

the matrix

A.

o:lt

?,1

(c)

Evaluate

.4.-1

when

-d.

:

lz

0

1l

lo

4

ol

fr

o

2l

(d)

Drptain

Gauss-elimination

method

to

solve

a set of

simultaneous

equations.

(4X6=20

Marks)

(b)

Differentiate

between

continuum

method

and finite

element

mettrod.

(8

Marks)

3.

(a)

A

rectangular

bar

in subjected

to an axial

load

P

as shown

in fig.l.

Derive

an

expression

for

potential

energr

and

hence

determine

the

extreme

value

of the

potential

9le-1ry

forthe-following

data. Modutus

of

elasticity

E

:200Gpa,

load

P

-

SkNr

length

of

the

bar

I

:

L00mm,

width

of

the

ba;

b

:20mm

arrd

thickness

of

the bar

t

:

Llmm. Also

state

its

equilibrium

stability.

.

,

2.

(a)

What

is finite

element method?

finite

element

analysis.

Drplain

the

basic

steps in

the formulation

of

(12

Marks)

iff

l_

T

-+

'L

Fta,

I

(b)

use

Rayleigh-Ritz

method

to find

the

disptacement

and the

stress

.,tilIill

point

of

the rod

as

shown

in

fig.2.

The

area of

cross

section

of

the bar

is 4OO

mmz

and. the

modulus

of elasticity

of the

material

is

7O

GPa.

Assume

the

displacement

to

be second

degree

polynomial.

(to

Marks)

-Explain

the

elimination

approach

for

handling

the

specified

displacement

boundary

conditions

(5

Marks)

4.

(a)

Contd....

2


32/33

ME6F.1

Page

No...

2

5.

(a)

(b)

(b)

Determine

the

nodal

displacements,

element

stresses,

and

suPport

reactions

of

'-'

thtrnuliy

loaded

bar

ai

shown

in

fig3"^Usi

elimination

method

for

handling

the

bound.ry;;;;itio.o.

rrr."

E

:"200Gpa

aad

load

P

:

300&N.

.

Fir"3

state

tJre

assumptions

made

in

the

analysis

of trusses.

(15

Marks)

(5

Marks)

For

the

three-bar

t1ass

shown

in

fig.4,

determine the nodal

{i9pl1rments

and

ror

the

three-bar

tmss

shown

in

fig.4,

determine the nodal

{i9pl15n

tfre

stre"s

in

each

member.

Take

Inodulus

of

elasticity

as

2OO

GPa'

lTo

?

Documents

Fem Questionpapers