Categories: Fourth Year First Semester (4-1)

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

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