Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech Mech Eng 1st Semester 74716 FINITE ELEMENT ANALYSIS Question Paper.

Roll No. Total No. of Pages : 2

Total No. of Questions : 08

M.Tech (ME) (2017 Batch) (Sem.?1)

FINITE ELEMENT ANALYSIS

Subject Code : MTME-102

M.Code : 74716

Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE questions in all.

2. Each question carries TWENTY marks.

1. Discuss the general procedure for finite element analysis of physical problems. How does

FEA differ from exact solutions approach for solving boundary value problems in

engineering?

2. Derive relation for expressing strain energy as product of strain energy density and total

volume of deformed material for a fixed bar element subjected to load. Using the work-

strain energy relation, obtain the governing equations for the bar element using

Castigliano?s theorem.

3. A structure consisting of two bars is shown in Fig. 1. An axial load P = 200 kN is applied

as shown. Determine the (a) element stiffness matrix (b) global stiffness matrix (c) global

load vector (d) stress in each bar and (e) reaction forces.

FIG. 1

4. Analyze a simply supported beam subjected to a uniformly distributed load throughout

using Rayleigh Ritz method. Adopt one-parameter trigonometric function. Evaluate the

maximum deflection and bending moment and compare with the exact solution.

1

2

P

100 mm 200 mm

Steel

A = 1000 mm

1

2

E = 200 Gpa

1

Bronze

A = 2000 mm

1

2

E = 83 Gpa

1

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1 | M-74716 (S9)-2711

Roll No. Total No. of Pages : 2

Total No. of Questions : 08

M.Tech (ME) (2017 Batch) (Sem.?1)

FINITE ELEMENT ANALYSIS

Subject Code : MTME-102

M.Code : 74716

Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE questions in all.

2. Each question carries TWENTY marks.

1. Discuss the general procedure for finite element analysis of physical problems. How does

FEA differ from exact solutions approach for solving boundary value problems in

engineering?

2. Derive relation for expressing strain energy as product of strain energy density and total

volume of deformed material for a fixed bar element subjected to load. Using the work-

strain energy relation, obtain the governing equations for the bar element using

Castigliano?s theorem.

3. A structure consisting of two bars is shown in Fig. 1. An axial load P = 200 kN is applied

as shown. Determine the (a) element stiffness matrix (b) global stiffness matrix (c) global

load vector (d) stress in each bar and (e) reaction forces.

FIG. 1

4. Analyze a simply supported beam subjected to a uniformly distributed load throughout

using Rayleigh Ritz method. Adopt one-parameter trigonometric function. Evaluate the

maximum deflection and bending moment and compare with the exact solution.

1

2

P

100 mm 200 mm

Steel

A = 1000 mm

1

2

E = 200 Gpa

1

Bronze

A = 2000 mm

1

2

E = 83 Gpa

1

2 | M-74716 (S9)-2711

5. The differential equation for a phenomenon is given by (d

2

y/dx

2

) + 500x

2

= 0; 0 ? x ? 5.

The boundary conditions are y(0) = 0 and y(5) = 0. Find the approximate solution using

any classical technique. Start with minimal possible approximate solution.

6. Develop a one-dimensional finite element model of heat transfer including both

conduction and convection for a solid cylindrical body surrounded by a fluid medium.

Assume boundary conditions.

7. A fin having rectangular cross-section 4 cm wide and 1 cm thick is 8 cm long. The fixed

end of the fin is exposed to a temperature of 100?C. Determine the temperature

distribution along the length of the fin, assuming that convection heat loss occurs from

the fin. Given k = 3 W/cm?C, h = 0.1 W/cm

2

?C and surrounding fluid temperature is

20?C.

8. Discuss the use of stream functions and velocity potential functions in solving two-

dimensional, incompressible flow problems.

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 13 December 2019