Download Visvesvaraya Technological University (VTU) BE ( Bachelor of Engineering) ME (Mechanical Engineering) 2015 Scheme 2020 January Previous Question Paper 6th Sem 15ME61 Finite Element Method
15ME61
Sixth Semester S.E. Degree Examination, Dec.24-94n.2020
Finite Element Method
Time: 3 hrs. Max. Marks: 80
Note: Answer FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. List the type of elements with neat sketch. (06 Marks)
73 b. A simply supported beam subjected to point load at the centre. Derive an equation for
maximum deflection using trigonometrically function by RR method. (10 Marks)
-0
q)
OR
ll
2 a. List the advantages and disadvantages of FEM.
c ?
b. Explain Elasticity matrix [D] for stress and plain strain.
.., .--
-.... ,...-
c. Explain simplex, complex and multiplex elements.
._...-.0 r
th
.
c
-
Module-2
_ -
3 a. Derive the shape function, in natural coordinate system for:
c.. -
V
--
,., .
(i) Constant strain triangle.
...
..= . : (ii) I D bar element. (08 Marks)
0 -
.
...
b. Using two point Gaussian quadrature formula evaluate and compare with exact solution:
,i
,,,
4
,
0
E 7.
(i)
I = f (I + +2
2
+ 3V k I
,..., t
,
-1
T5 G
42
6 -0
03 0
(ii) I = .1 (4 ? y)
2
dy (08 Marks) "
4
--
-'5 t
2
7=z,
OR
>, t,
4 a. For the stepped bar shown in Fig. Q4 (a), determine the nodal displacement, element stresses
iE
:-: _,.. .
0
and reaction at supports.
E
1
= 70 GPa; E2 = 200 GPa; P = 200 KN; A
l
= 2400 mm
2
; A2 = 600 mm
2
(08 Marks)
-= ,-
Z '2
.
:, ;:,
CA '..=
= ',.-:,
CC r-
L. E,
g'
72
>.,,..-
0
t.0
0 t.0
1; ?
.
E >
0 e
<
0
z -
5co
Fig. Q4 (b)
1 of 2
(03 Marks)
(04 Marks)
(09 Marks)
'I c
Fig. Q4 (a)
b. A plane truss shown in Fig. Q4 (b), determine nodal displacements, stresses in each element
and reaction at supports.
E = 200 GPa ; A
l
= 1200 111111
2
; Ai! = 1000 mm
2
; P = 50 KN (08 Marks)
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USN
15ME61
Sixth Semester S.E. Degree Examination, Dec.24-94n.2020
Finite Element Method
Time: 3 hrs. Max. Marks: 80
Note: Answer FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. List the type of elements with neat sketch. (06 Marks)
73 b. A simply supported beam subjected to point load at the centre. Derive an equation for
maximum deflection using trigonometrically function by RR method. (10 Marks)
-0
q)
OR
ll
2 a. List the advantages and disadvantages of FEM.
c ?
b. Explain Elasticity matrix [D] for stress and plain strain.
.., .--
-.... ,...-
c. Explain simplex, complex and multiplex elements.
._...-.0 r
th
.
c
-
Module-2
_ -
3 a. Derive the shape function, in natural coordinate system for:
c.. -
V
--
,., .
(i) Constant strain triangle.
...
..= . : (ii) I D bar element. (08 Marks)
0 -
.
...
b. Using two point Gaussian quadrature formula evaluate and compare with exact solution:
,i
,,,
4
,
0
E 7.
(i)
I = f (I + +2
2
+ 3V k I
,..., t
,
-1
T5 G
42
6 -0
03 0
(ii) I = .1 (4 ? y)
2
dy (08 Marks) "
4
--
-'5 t
2
7=z,
OR
>, t,
4 a. For the stepped bar shown in Fig. Q4 (a), determine the nodal displacement, element stresses
iE
:-: _,.. .
0
and reaction at supports.
E
1
= 70 GPa; E2 = 200 GPa; P = 200 KN; A
l
= 2400 mm
2
; A2 = 600 mm
2
(08 Marks)
-= ,-
Z '2
.
:, ;:,
CA '..=
= ',.-:,
CC r-
L. E,
g'
72
>.,,..-
0
t.0
0 t.0
1; ?
.
E >
0 e
<
0
z -
5co
Fig. Q4 (b)
1 of 2
(03 Marks)
(04 Marks)
(09 Marks)
'I c
Fig. Q4 (a)
b. A plane truss shown in Fig. Q4 (b), determine nodal displacements, stresses in each element
and reaction at supports.
E = 200 GPa ; A
l
= 1200 111111
2
; Ai! = 1000 mm
2
; P = 50 KN (08 Marks)
1? 5 r 1.?rn
xn
Jw
6
-
rei
15ME6t
Module-3
5 a. Derive the Hermite function of a beam element. (08 Marks)
b. For the beam element shown in figure Q5 (b), determine the displacement and slope at the
free end. Take E = 70 GPa, I = 4x I V m
4
(08 Marks)
10O Xrt
o'F- T
4
\ YIN
r
Fig. Q5 (b)
OR
6 a. Derive the stiffness matrix for a torsion element. (06 Marks)
b. Find the deflection and slopes at the nodes for the aluminium beam shown in Fig. Q6 (b).
(10 Marks)
Fig. Q6 (b)
E = 70 GPa
I =2x10
-6
m
4
Module-4
7 a. With brief explanation obtain the rate equation that describes the rate of energy flow for the
following conditions:
(i) Conduction (ii) Convection (iii) Radiation (06 Marks)
b. Derive the shape function of a 1 D bar element with temperature T
1
and T2 at the nodes.
(10 Marks)
OR
8 a. Determine the temperature distribution in the rectangular fin shown in Fig. Q8 (a). Neglect
convection heat transfer and assume heat generated inside the fin as 500 W/m
3
(08 Marks)
0.
02.
WI
0.0ym
Fig. Q8 (a)
b.
Derive the stiffness matrix for fluid flow in 1 D bar element. (08 Marks)
Module-5
9 Derive the shape function for axisymmetric triangular element. (16 Marks)
OR
10 Derive the consistent mass matrix for the following:
(i)
1 D bar element.
(ii) 1 D truss element.
/ '
`'N (16 Marks)
2 of 2
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This post was last modified on 02 March 2020