FEA 16 MARKS QUESTIONS.docx

7/26/2019 FEA 16 MARKS QUESTIONS.docx

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ME 6603- Finite Element Analysis

16 MarksUNIT- I

1. Determine using any weighte resiual te!hni"ue the tem#erature istri$uti%n al%ng a !ir!ular &in

%& length 6 !m an raius 1 !m. the &in is atta!he t% a $%iler wh%se wall tem#erature is 1'0(! an

the &ree en is insulate. Assume !%n)e!ti%n !%e&&i!ient h*10 +,!m (!.!%nu!ti%n !%e&&i!ient k*0

w, !m(! an T * '0(!. the g%)erning e"uati%n &%r the heat trans&er thr%ugh the &in is gi)en $y

Assume a##r%#riate $%unary !%niti%ns an !al!ulate the tem#eratures at e)ery 1 !m &r%m the

le&t en. /AU MA,2UNE-014

. Deri)e the g%)erning e"uati%n &%r a ta#ere r% &i5e at %ne en an su$e!te t% its %wn sel&

weight an a &%r!e # at the %ther en as sh%wn in &ig. let the length %& the $ar $e l an let the !r%ss

se!ti%n )ary linearly &r%m A1 at the &i5e en t% A at the &ree en. E an y re#resent the y%ungs

m%ulus an s#e!&i! weight %& the msterial %& the $ar. 7%n)ert this e"uati%n int% its weak &%rm an

hen!e etermine the matri!es &%r s%l)ing using thr rit8 te!hni"ue. /AU MA,2UNE-014


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3. Using !%ll%!ati%n meth%9&in the ma5imum is#la!ement %& the ta#ere r% as sh%wn in &ig E*

:10 N,!m9y * 0.0 N,!m. /AU N;


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'. 7%nsiser the $ar sh%wn in &ig etermine the n%al is#la!ements9 element stresses an su##%rt

rea!ti%ns. /AU N;


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6. The i&&erential e"uati%n %& a #hysi!al #hen%men%n is gi)en $y

The $%unary !%niti%ns are >

%$tain %ne term a##r%5imate s%luti%n $y using galerkins meth% %& weighte resiuals.

/AU MA,2UNE-01'4

. De)el%# the weak &%rm an etermine the is#la!ement &iel &%r a !antile)er $eam su$e!te t% a

uni&%rmly istri$ute. =%a an a #%int l%a a!ting at the &ree en. /AU N;


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?. 7%nsier a #alne wall with a uni&%rmly istri$ute heat s%ur!e.%$tain the &inite element

&%rmulati%n &%r the a$%)e !ase $ase %n the stat%i%nary %& a &un!ti%nal. /AU N;


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10. A sim#ly su##%rte $eam su$e!te t% uni&%rmly istri$ute l%a %)er entire s#an an it is

su$e!te t% a #%int l%a at the !entre %& the s#an. 7al!ulate the e&el!ti%n using rayleigh rit8meth% an !%m#are with e5a!t s%luti%ns.

/AU MA,2UNE-0134


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11. BiC Des!ri$e the hist%ri!al $a!kgr%un %& FEM.

BiiC e5#lain the rele)an!e %& FEA &%r s%l)ing esign #r%$lems with the ai %& e5am#les. /AU

N;


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BiiC s%l)e the %rinary i&&erential

u$e!t t% the $%unary !%niti%ns yB0C * yB1C*0 using galerkin meth% with trial &un!ti%ns n0B5C *

0 G N1B5C * 5B1-5C /AU MA,2UNE-0134

1'. BiC is!uss the &a!t%rs t% $e !%nsiere in e!retisati%n %& a %mine.

BiiC s%l)e the &%ll%wing e"uati%ns using the gauss eliminati%n meth%.

/AU MA,2UNE-0134


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1. The i&&erential e"uati%n &%r a #hen%men%n is gi)en $y

The $%unary !%niti%ns are yB%C * 0 9 yBC * 0 &in the a##r%5imate s%luti%n using any !lassi!alte!hni"ue . tart with minimal #%ssi$le a##r%5imate s%luti%n. /AU MA,2UNE-014

16. BiC =ist an $rie&ly es!ri$e the general ste#s %& &inite element meth%.


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BiiC Deri)e an e"uati%n t% &in the is#la!ement at n%e %& &i5e &i5e $eam su$e!te t% a5ial

l%a # at n%e using Hayleigh rit8 meth%.

/AU MA,2UNE-014


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1. Deri)e the !hara!teristi! e"uati%ns &%r the %ne imensi%nal $ar element $y using #ie!e wise

e&ine inter#%lati%ns an weak &%rm %& the weighte resiual meth% /AU MA,2UNE-014

1?. BiC Deri)e the element le)el e"uati%n &%r %ne imensi%nal $ar element $ase %n the stati%nary %& a

&un!ti%nal.

BiiC =ist %ut the general #r%!eure &ir FEA #r%$lems. /AU MA,2UNE-014


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1@. An all%y 1 m l%ng an 00 mm in !r%ss se!ti%n is &i5e at %ne en is su$e!te t% a !%m#ressi)e

l%a %& 0 JN. I& the m%ulus %& elasti!ity &%r the all%y is 100 a9 &in the e!rease in the length %&

the $ar. Als% etermine the stress e)el%#e an the e!rease in length at 0.m9 0. m an 0. m.

s%l)e $y !%ll%!ati%n meth%. /AU N;


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0. An all%y 1 m l%ng an 00 mm in !r%ss se!ti%n is &i5e at %ne en is su$e!te t% a !%m#ressi)e

l%a %& 0 JN. I& the m%ulus %& elasti!ity &%r the all%y is 100 a9 &in the e!rease in the length %&

the $ar. Als% etermine the stress e)el%#e an the e!rease in length at 0.m9 0. m an 0. m.

s%l)e $y Hit8 meth%. /AU N;


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1. E5#lain the #r%!ess %& is!retisati%n %& a stru!ture in &inite element meth% in etail9 with suita$le

illustrati%ns &%r ea!h as#e!t $eing is!usse. /AU N;


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. A uni&%rm r% su$e!te t% a uni&%rm a5ial l%a is illustrate in &ig 9 the e&%rmati%n %& the $ar is

g%)erne $y the i&&erential e"uati%n gi)en $el%w. Determine the is#la!ement using weighte

resiual meth%.

/AU MA,2UNE-0114


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3. Fin the n%al is#la!ement an element stresses &%r the $ar sh%wn in &ig

/AU MA,2UNE-0114


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'. Dis!uss the &%ll%wing meth%s t% s%l)e the gi)en i&&erential e"uati%n>

+ith the $%unary !%niti%ns yB0C * 0 an yBKC * 0

BiC


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6. Analy8e a sim#ly su##%rte $eam su$e!te t% a uni&%rmly istri$ute l%a th%ught using

Hayleigh Hit8 meth%. A%#t %ne #arameter trig%n%metri! &un!ti%n. e)aluate the ma5imum

e&le!ti%n an LM an !%m#are with the e5a!t s%luti%n.

/AU N;


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. %l)e the &%ll%wing set %& simultane%us e"uati%n $y aussian eliminati%n meth%

/AU N;


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?. A sim#ly su##%rte $eam Bs#an = an &le5ural rigiity EIC !arries tw% e"ual !%n!entrate l%as at

ea!h %& the "uarter s#an #%ints. Using Hayleigh Hit8 meth% etermining the e&le!ti%n uner the

tw% l%as an tw% en sl%#es.

/AU MA,2UNE-00@4

@. Use the aussian eliminati%n meth% t% s%l)e the &%ll%wing simultane%us e"uati%ns>

/AU MA,2UNE-00@4


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30. BiC what is !%nstituti)e relati%nshi# E5#ress the !%nstituti)e relati%ns &%r a linear elasti! is%tr%#i!

material in!luing initial stress an strain.

BiiiC !%nsier the i&&erential e"uati%n

&%r su$e!te t% $%unary !%niti%ns yB0C

* 09yB1C *0

The &un!ti%nal !%rres#%ning t% this #r%$lem t% $e e5tremi8e is gi)en $y

&in the s%luti%n %& the #r%$lem using Hayleigh

rit8 meth% $y !%nsiering a tw% term s%luti%n as yB5C *!5B1-5C !5B1-5C

/AU N;


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31. BiC

/AU N;


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BiiC %l)e the &%ll%wing system %& e"uati%ns using gauss eliminati%n meth% .

/AU N;


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3. E5#lain the aussian eliminati%n meth% &%r s%l)ing %& simultane%us linear alge$rai! e"uati%ns

with e5am#les.

33. /AU MA,2UNE-00?4

3'. A !antile)er $eam %& length = is l%ae with a #%int l%a at the &ree en. Fin the ma5imum

e&le!ti%n an ma5imum $ening m%ment using Hayleigh rit8 meth% using the &un!ti%n

/AU MA,2UNE-00@4


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3. 7%m#ute the )alue %& !entral e&le!ti%n &igure $y assuming 9 The $eam is uni&%rm thr%ugh an

!arries a !entral #%int l%a.


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36. BiC +rite sh%rt n%te %n galerkins meth%.

BiiC +rite $rie&ly a$%ut aussian eliminati%n. /AU N;


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UNIT- II

1. Determine the ma5imum e&le!ti%n an sl%#e in the $eam9 l%ae as sh%wn in &ig . Determine als%

the rea!ti%ns at the su##%rts. E* 00#a 9I* 0 10-6 m' * JN,m an =*1m

/AU MA,2UNE-014

. Deri)e using lagrangian #%lyn%mials the sha#e &un!ti%ns &%r %ne imensi%nal three n%e $ar

element. #l%t the )ariati%n %& the same . Ken!e eri)e the sti&&ness matri5 an l%a )e!t%r.

/AU MA,2UNE-014


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3. 7%m#uter the sl%#e9 e&le!ti%n an rea!ti%n &%r!es &%r the !antile)er $eam %& length O=P !arrying

uni&%rmly istri$ute l%a %& intensity &%. /AU N;


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'. Determine the n%al is#la!ements9 stress an strain &%r the $ar sh%wn in &ig

/AU N;


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. A tw% n%e truss element is sh%wn in &ig 9 the n%al is#la!ements are U1* mm an u *?mm.

!al!ulate the is#la!ement at 5*l,'9l,3 an l,.

/AU MA,2UNE-01'4

6. F%r the tw% truss sh%wn in &ig 9 etermine the is#la!ements %& n%e 1 an the stress in element 1-

3.

/AU MA,2UNE-0134


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. Deri)e the sti&&ness matri5 an $%y &%r!e )e!t%r &%r a "uarati! s#ar element.

/AU N;


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?. Analy8e the $eam sh%wn in &ig using &inite element te!hni"ue. Determine the r%tati%ns at the

su##%rts. i)en E* 00a an I*'106 mm'

/AU N;


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@. Determine the e5tensi%n %& the $ar sh%wn in &ig 9 ue t% sel& weight an a !%n!entrate l%a %&

600N a##lie at its en. gi)en L1*00mm 9$ *100mm an t*0mm.use tw% s#ar elements t% s%l)e

the #r%$lem. take E*10 N,mm an g*0.?10-' N,mm.

/AU N;


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10. A !antile)er $eam %& length 3.' m has an elati! s#ring su##%rt %& sti&&ness 30 JN,m at its &ree en9

where a #%int l%a %& 13 JN a!ts.Take y%ungs m%ulus as 00 a an area m%ment %& inertia %&

the !r%ss se!ti%n as 110-' m' .etermine the is#la!ement an sl%#e at the n%e an the rea!ti%ns.

/AU N;


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1. F%r the $eam sh%wn in &ig 9 etermine BiC the sl%#es at n%e an 3 an

BiiC )erti!al e&le!ti%n at the mi-#%int %& the istri$ute l%a. All the elements ha)e E*00a an

I*106 mm'.

/AU MA,2UNE-0134


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13. Determine the is#la!ements an sl%#es at the n%es &%r the $eam sh%wn in &ig. take k*00JN,m9

E*0a an I*10-' m'.

/AU N;


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1'. Determine the n%al is#la!ements an sl%#es &%r the $eam sh%wn in &ig. &in the m%ment at the

mi#%int %& element 1. /AU N;


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1. A ta#ere $ar %& aluminimum is ha)ing a length %& 00 7m. The area %& !r%ss se!ti%n at the &i5e

en is ?0 !m an the &ree en is 0!m with the )ariati%n %& the se!ti%nal area as linear. The $ar I

su$e!te t% an a5ial l%a 10 JN at '0 mm &r%m the &i5e en. 7al!ulate the ma5imum

is#la!ement an stress e)el%#e in the $ar. /AU N;


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1. Determine the sha#e &un!ti%n an element matri!es &%r "uarati! $ar element.

/AU MA,2UNE-014


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1?. Fin the n%al is#la!ement e)el%#e in the #laner truss sh%wn in &ig when a )erti!ally

%wnwar l%a %& 1000 N is a##lie at n%e '. The re"uire ata are gi)en in the ta$le 1.

/AU MA,2UNE-

014


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.

1@. F%r the #lane trusses su##%rte $y the s#ring at n%e 1 in &ig etermine the n%al is#la!ement

an stresses in ea!h elemnt. =et E*10#a an A*.010-' m.

/AU MA,2UNE-014

.

0. A !%nsente l%a *0 JN is a##lie at the !entre %& a &i5e $eam %& length 3 m 9e#th 00 mm

an with 10 mm. !al!ulate the e&le!ti%n an sl%#e at the mi#%int. Assume E*10 N,mm.

/AU MA,2UNE-014


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1. 7al!ulate n%al is#la!ement an elemental stresses &%r the truss sh%wn &ig E*0a !r%ss

se!ti%nal area A*!m &%r all truss mem$ers.

/AU MA,2UNE-0114


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. Esta$lish the sha#e &un!ti%ns %& an eight n%e "uarilateral element an re#resent them

gra#hi!ally.

/AU MA,2UNE-0114


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3. enerate the sti&&ness matri5 %& a n%e #rismati! $ar with %ne egree %& &ree%m at ea!h n%e.

/AU N;


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'. Deri)e the !%nsistent l%a )e!t%r &%r a &i5e $eam su$e!te t% uni&%rmly istri$ute l%a

thr%ugh. use sha#e &un!ti%ns !%rres#%ning t% tw% egrees %& &ree%m at ea!h %& the tw% n%es %&

the element. A5ial e&%rmati%ns !an $e negle!te. /AU N;


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6. Deri)e the inter#%lati%n &un!ti%n &%r the %ne imensi%nal linear element with a length O=P an tw%

n%es9 %ne at ea!h en 9 esigne as I an assume the %rigin %& the !%%rinate system is t% the le&t

%& n%e i./AU N;


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. A !%lumn %& length 00 mm is l%ae a5ially as sh%wn in &ig. analy8e the !%lumn an e)aluate the

stress an strains at salient #%ints. The y%ungPs m%ulus !an $e taken as E. A1*6. mm A *1

mm.

/AU MA,2UNE-00@4

?. F%r the #rismati! $ar sh%wn &ig generate the sti&&ness matri5 !%rres#%ning t% the three

!%%rinatePs inia!ate.use the &%ll%wing sha#e &un!ti%ns.

/AU MA,2UNE-00@4


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@. The ste##e $ar sh%wn in &ig is su$e!te t% an in!rease in tem#erature T * ?0 ! . Determine the

is#la!ements9 elements stresses an su##%rt rea!ti%ns.

/AU N;


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30. 7%nsier a tw% $ar truss su##%rts $y a s#ring sh%wn in 9 $%th $ars ha)e E* 10A an

A*.010-' m. Lar %ne has a length %& m an tw% has a length %& 10 m. the s#ring sti&&ness is k*

JN,m. etermine the h%ri8%ntal an )erti!al is#la!ements at the %int 1 an stresses in ea!h $ar.

/AU N;


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31. BiC Deri)e the sha#e &un!ti%ns &%r a D $eam element. B?C

BiiC Deri)e the sha#e &un!ti%ns &%r a D Truss element. B?C /AU MA,2UNE-00?4


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3. Ea!h %& the &i)e $ars %& the #in %inte truss sh%wn in &ig9 has a !r%ss se!ti%nal area 0 s".!m

an E*00a. /AU MA,2UNE-00?4

33. +hy higher %rer elements are neee Determine the sha#e &un!ti%ns %& an eight n%e

re!tangular element.

/AU MA,2UNE-004


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UNIT III

1.

.

3. BiC a $ilinear re!tangular element has !%%rinates as sh%wn in &ig. an the n%al tem#eratures are

T1 * 100 7 9 T * 60 !9 T3 * 0 7 9 T'* @0 !. !%m#ute the tem#erature at the #%int wh%se

!%%rinates are B.9.C. als% etermine the ?0 7 is%therm.


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BiiC Use gauss "uarature e)aluate the &%ll%wing integral

/AU MA,2UNE-014

'. F%r the &%ur n%e element sh%wn in &ig. etermine the a!%$ian an e)aluate its )alue at the

#%intB1,91,3C


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/AU MA,2UNE-014


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. BiC eri)e the a!%$ian matri5 &%r triangular element with the B59yC !%%rinates %& the n%es are

B1.9C9B93.C an B'9C at n%es I99k. /AU N;


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. Determine the sha#e &un!ti%ns N19N an N3 at the interi%r #%int # &%r the triangular element

sh%wn in the &igure.

/AU MA,2UNE-01'4

?. Determine the sha#e &un!ti%ns &%r a !%nstant strain triangular B7TC element in terms %& natural

!%-%rinate system. /AU MA,2UNE-01'4


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@. Esta$lish the $%y &%r!e an tra!ti%n &%r!e BUD=C )e!t%r &%r a l%wer %rer "uarilateral element.

/AU N;


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11. 7al!ulate the )alue %& #ressure at #%int A whi!h is insie the 3 n%e triangular element as sh%wn

in &ig .the n%al )ari%us are a1 * '0 Ma 9a * 3' Ma an a3 * '6 Ma9 #%int A is l%!ate at

B91.C . assume #ressure is linearly )arying in the element. Als% etermine the l%!ati%n %& ' Ma

!%nt%ur line. /AU MA,2UNE-0134

1. F%r the #lane stress element wh%se !%-%rinates are gi)en $y B1009100C9B'009100C an B009'00C the

n%al is#la!ements are u1* .0 mm 9 )1 * 1.0 mm9 u*1.0 mm9 )* 1. mm9 )3* 0. mm9 u3* .

mm . Determine the element stresses. Assume E * 00 N,man t*10 mm. all !%%rinates are in

mm. /AU MA,2UNE-0134


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13. Deri)e the !hara!teristi! matri5 &%r a tw% imensi%nal heat !%nu!ti%n #r%$lem using triangular

element $y galerkin a##r%a!h. /AU N;


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1'. 7%nsier a re!tangular #late %& length 300 mm an with 00 mm ha)ing a thi!kness %& 300

mm. it is su$e!te t% a uni&%rm heat s%ur!e %& 00 +,m3 a!ting %)er the wh%le $%y. The

tem#erature %& the t%# sie %& the $%y is maintaine at 130 !. the $%y is insulate %n the %ther

eges. Take the thermal !%nu!ti)ity %& the material ass 3 +,m!. Determine the tem#erature

istri$uti%n using triangular elements. /AU N;


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16. Determine the element matri!es an )e!t%rs &%r the =T element sh%wn in &ig. the n%al

!%%rinates are iB191C 9 B9C an kB39C !%n)e!ti%n takes #la!e al%ng the ege k.

/AU MA,2UNE-01347LE


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1. 7al!ulate n%al is#la!ement an elemental stresses &%r the truss sh%wn in &ig9 E*0 a !r%ss

se!ti%nal area A* !m &%r all truss mem$ers. /AU N;


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1@. 7%nsier the triangular element sh%w in &ig 9 the element is e5tra!te &r%m a thin #late %&

thi!kness 0. !m . the material is h%t r%lle l%w !ar$%n steel. The n%al !%-%rinates are 51*0 yi *0

5 *09 y*-1 5k * an& yk * -1 !m. etermine the elemental sti&&ness matri5 . assuming #lane stress

analysis. Take u*0.3 an E* .1510 N,!m.

/AU MA,2UNE-014

0.


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/AU MA,2UNE-014

1.

/AU N;


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.

/AU N;


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3.

/AU MA,2UNE-0147LE


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'.

/AU MA,2UNE-0147LE


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.

/AU MA,2UNE-0114


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6.

/AU MA,2UNE-0114


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. A !ertain #r%$lem %& %ne imensi%nal steay heat trans&er with a istri$ute heat s%ur!e is

g%)erne $y the e"uati%n

/AU N;


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@. Determine three #%ints %n the 0 7 !%nt%ur line &%r the re!tangular element sh%wn in &ig 9 the

n%al )alues are "i * ' !9 " * ' !9 "k * 6 ! an "m * '6 !.

/AU MA,2UNE-0104


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30.

/AU MA,2UNE-0104


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31.

/AU N;


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/AU N;


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3'. 7al!ulate the tem#erature istri$uti%n in stainless steel &in sh%wn in &ig the regi%n !an $e

is!reti8e int% elements an 6 n%es. /AU MA,2UNE-00@4

3.


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/AU MA,2UNE-00?4

36.

/AU MA,2UNE-00?4


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3.

/AU MA,2UNE-004


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3?.

/AU MA,2UNE-004


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UNIT I

FEA 16 MARKS QUESTIONS.docx

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