fea question bank - me 6603

7/26/2019 Fea Question Bank - ME 6603

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UNIT 2

1. A two noded truss element is shown in Figure. The nodal displacements are u 1 = 5 mm and

u2= 8 mm. Calculate the displacement at =1

4

1

31

2

!1"#

2. For the two $ar truss shown in Figure% determine the displacements o& node 1 and the stress

in element 1'(. !1"#

(. )eri*e the shape &unctions &or one dimensional linear element using direct method. !1"#

+. The loading and other parameters &or a two $ar truss element is shown in Fig. )etermine

!i# The element sti&&ness matri &or each element

!ii# ,lo$al sti&&ness matri

!iii# Nodal displacements

!i*# -eaction &orces

!*# the stress induced in the elements. Assume =2// ,0a. !1"#

5. )etermine the shape &unction and element matrices &or uadratic $ar element. !1"#

". )eri*e the shape &unctions &or a 2) $eam element. !8#

. )eri*e the sti&&ness matri &or 2) truss element. !8#

8. 3rite the mathematical &ormulation &or a stead4 state heat trans&er conduction pro$lem and

deri*e the sti&&ness and &orce matrices &or the same. !1"#

. A tapered $ar o& aluminium is ha*ing a length o& 5// cm. The area o& cross section at the

&ied end is 8/ cm2and the &ree end is 2/ cm 2with the *ariation o& the sectional area as

linear. The $ar is su$6ected to an aial load o& 1/ 7N at 2+/ mm &rom the &ied end.

Calculate the maimum displacement and stress de*eloped in the $ar. !1"#

1/. A &ied $eam A o& 5 m span carries a point load o& 2/ 7N at a distance o& 2m &rom A.

)etermine the slope and de&lection under the load. Assume I = 1/ 9 1/(

7N' m2

. !1"#


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11. For the spring s4stem shown in Figure 1% calculate the glo$al sti&&ness matri%

displacements o& nodes 2 and (% the reaction &orces at node 1 and +. Also calculate the

&orces in the spring 2. Assume% 71= 7(= 1// N:m% 72= 2// N:m% u1=u+=/ and 0 = 5// N.

12. )eri*e an euation to &ind the displacement at node 2 o& &ied'&ied $eam su$6ected to

aial load 0 at node 2 using -a4leigh'-it; method.

1(. A concentrated load 0 = 5/ 7N is applied at the center o& a &ied $eam o& length ( m%

depth 2// mm and width 12/ mm. Calculate the de&lection and slope at the midpoint.

Assume = 2 9 1/5N:mm2

1+. A circular &in /& +/ mm diameter is &ied to a $ase maintained at 5/


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15. )etermine the maimum de&lection and slope in the $eam% loaded as shown in Figure.

)etermine also the reactions at the supports. = 2// ,0a% I=2/ 9 1/ '"m+% = 5 7N:m

and >= 1m.

1".

UNIT '1 INT-?)UCTI?N

1. An allo4 $ar 1m long and 2// mm2in cross section is &ied at one end is su$6ected to a

compressi*e load o& 2/ 7N. I& the modulus o& elasticit4 &or the allo4 is 1//,0a% &ind the

decrease in the length o& the $ar. Also determine the stress de*eloped and the decrease in

length at /.25m% /.5m and /.5m. @ol*e $4 collocation method. !1"#

2. An allo4 $ar 1m long and 2// mm2in cross section is &ied at one end is su$6ected to a

compressi*e load o& 2/ 7N. I& the modulus o& elasticit4 &or the allo4 is 1//,0a% &ind the

decrease in the length o& the $ar. Also determine the stress de*eloped and the decrease in

length at /.25m% /.5m and /.5m. @ol*e $4 -it; method. !1"#

(. )iscuss the &ollowing methods to sol*e the gi*en di&&erential euation

EI

d 2y

dx 2M(x )=0

with the $oundar4 conditions 4!/# = / and 4!B# = /

!i# ariational method !ii# Collocation method. !1"#

+. The di&&erential euation &or a phenomenon is gi*en $4d2y

dx2+500x 2 = 0;

/DD5.

The $oundar4 condition are 4!/# = /% 4!5#=/. Find the approimate solution using an4

classical techniue. @tart with minimal possi$le approimate solution.

5. )etermine using an4 3eighted -esidual techniue the temperature distri$ution along a

circular &in o& length " cm and radius 1 cm. The &in is attached to a $oiler whose walltemperature is 1+/


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3:cm2< C. Conduction coe&&icient = / 3:cm2


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UNIT G +

T3? )IHN@I?NA> CT?- 0-?>H@

1. )eri*e the Constituti*e matri &or ais s4mmetric anal4sis. !1/#

2. plain with an eample o& each o& the &ollowing

!1# @u$ 0arametric lement !2# Iso 0arametric lement

!(# @uper 0arametric lement

(. )e&ine $andwidth in &inite element anal4sis and its signi&icance in the solution o& glo$al

s4stem matrices.

+. For the plane strain elements shown in &igure% the nodal displacements are gi*en as u 1=

/.//5 mm% *1= /.//2 mm% u2= /./% *2= /./% u(= /.//5 mm% *(= /.(/ mm. )etermine the

element stresses and the principle angle. Ta7e = / ,pa and 0oissons ration = /.( and use

unit thic7ness &or plane strain. All coordinates are in mm.

5. sta$lish the traction &orce *ector and estimate the nodal &orces corresponding to a uni&orm

radial pressure o& $ar acting on an aiss4mmetric element as shown in &igure. Ta7e = 2//

,0a and 0oissons ratio = /.25

". )etermine the element

sti&&ness matri and the thermal load *ector &or the

plane stress element shown in &igure. The element eperiences 2/


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. For the plane strain element shown in the Figure% the nodal displacements are gi*en as u1=

/.//5 mm% u2= /.//2 mm% u(= /./ mm% u+=/./ mm% u5=/.//+ mm% u"= /./ mm. )etermine

the element stress. Ta7e = 2// ,pa and =/.(. Use unit thic7ness &or plane strain.

UNIT 5

I@?0A-AHT-IC >HNT

1. )eri*e the element characteristics o& a &our node uadrilateral element

2. )e&ine the &ollowing terms with suita$le eamples

!i# 0lane stress% 0lane strain !ii# Node% lement and @hape &unctions

!iii# Iso'parametric element !i*# Ais4mmetric anal4sis.

fea question bank - me 6603

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