JNTU Kakinada B-Tech 4-1 FINITE ELEMENT METHODS R13 March 2018 Question Paper

IV B.Tech I Semester Supplementary Examinations, February/March – 2018
FINITE ELEMENT METHODS (Common to Aeronautical Engineering, Automobile Engineering and Mechanical
Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Explain about plane stress and plane strain. [3]
b) Discuss about the elements used in discretization. (1D,2D,3D case). [3]
c) Write the Hermite shape functions of beam element and plot them. [4]
d) Write the advantages and applications of axisymmetric element. [4]
e) Explain about isoparametric and subparametric elements. [4]
f) Discuss about the softwares used to evaluate the problems in FEM [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss about different weighted residual methods with the help of an example. [8]
b) For the spring assemblages shown in figure 2 (b), determine the nodal
displacements by using the concept of potential energy.
Figure 2 (b)

[8]

3. a) Consider a simple one dimension structure with three elements, explain the
process of stiffness matrix and load vector assembly.
[8]
b) Discuss about the types of elements used in domain discritization. [4]
c) Write the properties of stiffness matrix. [4]

4. For the plane trusses shown in figure 4, determine the horizontal and vertical
displacements of node 1 and the stresses in each element. All elements have
E=210 GPa and A=4.0 X 10
-4
m
2
.
Figure 4

[16]
Code No: RT41033
Set No. 1
R13
1 of 2

IV B.Tech I Semester Supplementary Examinations, February/March – 2018
FINITE ELEMENT METHODS (Common to Aeronautical Engineering, Automobile Engineering and Mechanical
Engineering)Time: 3 hours Max. Marks: 70
Question paper consists of Part-A and Part-B
Answer ALL sub questions from Part-A
Answer any THREE questions from Part-B
*****

PART ?A (22 Marks)1. a) Explain about plane stress and plane strain. [3]
b) Discuss about the elements used in discretization. (1D,2D,3D case). [3]
c) Write the Hermite shape functions of beam element and plot them. [4]
d) Write the advantages and applications of axisymmetric element. [4]
e) Explain about isoparametric and subparametric elements. [4]
f) Discuss about the softwares used to evaluate the problems in FEM [4]

PART ?B (3×16 = 48 Marks)2. a) Discuss about different weighted residual methods with the help of an example. [8]
b) For the spring assemblages shown in figure 2 (b), determine the nodal
displacements by using the concept of potential energy.
Figure 2 (b)

[8]

3. a) Consider a simple one dimension structure with three elements, explain the
process of stiffness matrix and load vector assembly.
[8]
b) Discuss about the types of elements used in domain discritization. [4]
c) Write the properties of stiffness matrix. [4]

4. For the plane trusses shown in figure 4, determine the horizontal and vertical
displacements of node 1 and the stresses in each element. All elements have
E=210 GPa and A=4.0 X 10
-4
m
2
.
Figure 4

[16]
Code No: RT41033
Set No. 1
R13
1 of 2

5. For the two dimensional loaded plate shown in figure 5, determine the
displacements of node 1 and 2 and the element stresses using plane stress
conditions.
Figure 5

[16]

6. a) Derive the strain displacement matrix of two dimensional four noded
isoparametric elements.
[10]
b) Evaluate the integral by two and three point gauss quadrature rule.
dx x x x I
?
?
? ? ? ?
1
1
2 3
7 5 2

[6]

7. a) For the composite wall shown in figure 7 (a), determine the interface
temperatures considering three elements.
Figure 7 (a)

[12]
b) Derive the consistence mass matrix of a two node bar element. [4]

Code No: RT41033
Set No. 1
R13
2 of 2