# PTU B.Tech Aero Engineering? 6th Semester May 2019 72458 FINITE ELEMENT METHODS Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester Aerospace Engineering?

Roll No.
Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (2012 Batch) (Sem.?6)
FINITE ELEMENT METHODS
Subject Code : ASPE-313
M.Code : 72458
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.
4.
Assume suitably missing data if any.

SECTION-A
1.

a. Write the expression of six strain components in terms of displacements.

b. Differentiate between natural and Cartesian coordinate systems.

c. Explain the kinematically admissible displacement field term as being used in FEM.

d. Explain plain stress condition with one example.

e. Draw eight noded quadrilateral element in Cartesian and natural coordinate systems.

f. Explain Lagrange's shape functions/elements.

g. What is carried out in the processing module of FEM software?

h. What is super-parametric type of Finite Element formulation?

i. Write the equation of 2-D heat conduction problem in terms of temperature (T),

thermal conductivity (k) and heat source/sink (Q).

j. Differentiate between complex and multiplex elements with examples.

1 | M-72458

(S2)-1622

SECTION-B
2.
Explain the principle of minimum potential energy and virtual work with their relevant
equations.
3.
Derive the transformation matrix for a 2-D truss element which transforms elemental
local displacement to elemental global displacement.
4.
Explain convergence in reference to Finite Element Method. Also explain the different
conditions to achieve the same.
5.
Derive the stress-strain matrix for plane stress conditions from the basic concept.

2

6.
For 1-D bar element, transformation is given as
( x ? x ) ?1

which is used to
1

x ? x
2
1

relate x and Let the displacement field is interpolated as u( ) = N1q1 + N2q2 where
(
1 )
(
1 ? )
N cos
and N cos
. Plot the shape functions and develop the
1

2

4

4

strain-displacement matrix. Also develop elemental matrix (you need not to evaluate the
integrals).
SECTION-C
7.
Explain the Finite Element modeling and shape function for linear interpolation of
temperature field (1-D heat transfer element).
8.
For the two-bar truss as shown in Fig. 1, determine the displacement of node 1. Assume
for
both
members
E
=
70
GPa
and
Area
=
200
mm2.Assume
2
2
l
lm
?l
?lm

2
2
A E
lm
m
?lm
?m
e
e
k

where l and m have usual meanings.
2
2
L
?l
?lm
l
lm
e

2
2
?lm
?m
lm
m

12kN
500 mm
1
2
300 mm
3
400 mm

Fig. 1
2 | M-72458

(S2)-1622

9.
A Constant Strain Triangle (CST) element is shown in Fig. 2. The element is subjected to
a body force fx = x2 N/cm3. Determine the nodal force vector due to the body force.
Assume element thickness as 1 cm. The coordinates in the Fig. 2 are given in cm.

3 (0, 3)
e
1 (0, 0)
2 (4, 0)
Fig. 2

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