8/11/2019 Sem 2 1213 Final Exam

1/8

.

CONFIDENTIAL

${

H

r,

LM3

UNIVERSITI

TT]N

HUSSEIN

ONN

MALAYSIA

FINAL EXAMINATION

SEMESTER

II

SESSTON

201212013

COURSE

NAME

:

FINITE

ELEMENT

METHOD

BDA

4033140303

BACHELOR

OF

MECHANICAL

ENGINEERING

WITH

HONOURS

JUNE

2OI3

2

HOURS

and

30

MINUTES

PART

A: ANSWERALL

QUESTIONS

PART

B:

ANSWERTWO

(2)

QUESTIONS

ONLY

COURSE

CODE

PROGRAMME

EXAMINATION

DATE

DURATION

INSTRUCTION

THIS

PAPER

CONTAINS

EIGIIT

(8) PAGES

CONFIDENTIAL

8/11/2019 Sem 2 1213 Final Exam

2/8

BDA 4033/BDA

40303

PART

A - Basic

Comprehension

and

Understanding

(AIISWER ALL

Questions)

Ql

For SOLID

element

in finite element

analysis;

(a)

States

the

number

of

degree

of

freedom exist

in

each

node'

Q2

(3

Sketch

any

four

(4)

examples

of

SOLID

elements.

In the

sketches

you

have

to

write

the

names

of

the elernents

and

you

have

to

indicate

the

nodes clearly

and

also the

node

numbers

(12

marks)

(4

Illustrate

two

(2) examples

of

higher

order

SOLID

elements.

In the

Illustration,

write

the

names-of

the

elements

and

indicate

the

nodes

clearly

and

also

the

node

numbers

(6

marks)

Liquid

with

dynamic

viscosity

of

p= 0'5

N

s/m2

flows

through

the

piping network

from

node

I to

node

4

shown

in

fiCUifn

Q2.

The

pressure at

node

I

is

1600

Pa

and

at

node

4is0Pa.

(a) Analyse

the

flow

resistance

matrix

of

every

section'

(b)

Find

the

pressure

levels

at

node

2 and

3.

use

direct

elimination

reduce

the

order

of

matrix

and

to solve

the

unknown

pressure'

(2

marks)

(5 marks)

method

to

(15 marks)

8/11/2019 Sem 2 1213 Final Exam

3/8

BDA

4033/BDA

40303

PART

B

-

Analysis

and

Applications

(ANSWER TWO

Questions

OM,Y)

e3

A ffuss

two-dimensional

structure

and

the

loading

condition

are

shown

in

FIGLIRE

e3.

The material

elasticity of

the truss

is

E:70

GPa

and

the

ooss

section,

A:3

cm2

-

Element

Node

Node

I

I

2

2

I

3

a

J

I

4

(a)

(b)

(c)

(d)

(e)

Calculate

stiffiress

matrix

for every

element.

Assemble

every

single

stiffiress

matrices

in a

global

stiffness

matrix.

Considering

the

constraints,

modiff

the

global

stiffiress

matrix

and

force vectJr

by

implementing

either direct

elimination

method

method.

You

need

to

speciff

the

method

you

are

using

Calculate

the

displacements

of

the

nodes-

Calculate

the

stresses

of

all

the

elements.

node

2

and

node

3.

Draw

the

connectivity

table

for

element

1

and

element

2'

Find

the

element

stiffiress

matrix

for

element

1

and

element

2.

(10

marks)

(5

marks)

the

global

or

penalty

(10

marks)

(2

marks)

(3

marks)

(2

Marks)

(2 Marks)

(6

Marks)

Q4

The

beam

is

fixed

at

node

I and

3 and

has

a

roller

support

at

node

2.

Triangle

distributed

loading

are

applied

from

node

2 to

node

3.

The

value

of

young

modulus'

E

=

200

GPa

and

the

moment

of

inertia

I =

4 x

106

mma'

The

beam

and

loading

are

shown

in

FIGURE

Qa.

(a)

Determine

concentrated

force

and

moment

that

equivalent

to

distributed

load

at

(b)

(c)

(d)

(e)

Developthecompleteglobalstiffiressmatrixinformot[K][U]:[F].

(6

Marks)

Determine

the

nodal rotation

at node 2

and

the

vertical

deflection

at

the

midpoint

of

the distributed

load.

(14

Marks)

8/11/2019 Sem 2 1213 Final Exam

4/8

Qs

BDA 4033/BDA

40303

FIG1RE

Q5

shows

one

of CST

(constant

strain

triangular)

elements

with a

thickness

of I

mm.

The

material

has a

modulus

elasticity

E:200

GPa

and

the

Poison's

ratio

v

:

0.25.

(a)

Based

on the

information

above,

decide

the

problem case

whether

it

is

plane

sffess

or

plane

strain

and

state

why.

(4 marks)

(b)

Calculate

the

elasticity

matrix

(4

marks)

(c)

Calculate

the

area

of

element.

(4

marks)

(d) Analyse

the

strain

displacement

matrix

IBJ

of

the

element.

(4

marks)

(e)

Determine

the

stiffiress

matrix

of

the

element'

(6

marks)

(f)

Ifthenodaldisplacementsareknown.'utr=0tfrllr,rr12=

I

mm,

uts=2

illfiI,v1/

=

0

mm,

vtz=

|.5

fillllo

V13

=

1

mm,

find

the

elemental

stresses.

(8 marks)

8/11/2019 Sem 2 1213 Final Exam

5/8

BDA 4033/BDA

40303

FINAL

EXAMINATION

SEMESTER

/ SESSION

COURSE

: SEM

:

FEM

rr t2012i2013

PROGRAM

: 3BDD/4BDD

COURSE

CODE

:

BDA

4033/BDA

40303

I)

=,

lll.?l{rzu

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-

la;ftJl

7.2

m

FIGURE

03

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=-

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:

9.;ll

rrn

L

-

60trt

I")'-. lll.?,irnt

FIGT]RE

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8/11/2019 Sem 2 1213 Final Exam

6/8

BDA 4033/BDA

40303

FINAL

EXAMINATION

SEMESTER

/

SESSION

COURSE

sEM

II

/201212013

FEM

PROGRAM

:

3BDD/4BDD

COURSECODE

:

BDA4033/BDA40303

P=

12

kt{/tt

FIGURE

04

FIGTJRE

05

8/11/2019 Sem 2 1213 Final Exam

7/8

BDA 4033/BDA

40303

SEMESTER/SESSION

:

COURSE

:

FINAL

EXAMINATION

SEM

II

/ 20l2l2}l3

PROGRAM

: 3

BDD

i

4BDD

FEM

COLJRSE

CODE

:

BDA

4033/

BDA

40303

USEFUL

EQUATIONS

FLOW

NETWORK:

FLOW

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MATRD(

r'r

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8/11/2019 Sem 2 1213 Final Exam

8/8

BDA

4033/BDA

40303

FINAL

EXAMINATION

SEMESTER/SESSION

: SEMW}OI}I2OI3

PROGRAM

:

3BDD/4BDD

COURSE

:

FEM

COURSECODE:

BDA4O33/BDA4O3O3

USEFUL

EQUATIONS

CST

ELEMENT

Plane

Stress:

Plane

Strain:

rn--L-[';"

r]',,

3l

r",=i:l.'

il

o

r+l

.,

["*

o

.r,r

o

tu

ol

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tll

rl

"'l

rrr=E["',,

x

":

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r

It

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-

END

OF

QIIESTTONS

-