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

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.

Answer briefly :

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.

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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

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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

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any

page of Answer Sheet will lead to UMC against the Student.

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This post was last modified on 04 November 2019