M.E. DEGREE EXAMINATION, JUNE 2010

Second Semester

Engineering Design

ED9221 — FINITE ELEMENT METHODS IN MECHANICAL DESIGN

(Common to M.E. Computer Aided Design and M.E. Product Design and

Development)

(Regulation 2009)

Time : Three hours Maximum : 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. How will you obtain total potential energy of a system?2. Define discretization error.

3. What is a weighted integral statement? Give examples.

4. Express quadratic shape functions of a line element.

5. What is constant strain triangle? Why is it called so?

6. How can the bandwidth of a matrix be minimized?

7. Sketch a typical beam element showing degrees of freedom.

8. Give two examples of time dependent problems in elasticity.

9. State any two nonlinear problems in FEA.

10. Differentiate between material nonlinearity and geometric nonlinearity.

PART B — (5 × 16 = 80 Marks)

11. (a) Taking the stepped bar as an example, describe the step by stepprocedure of the finite element solution for obtaining the nodal

displacements and stresses. Clearly indicate the procedure for

information and representation of nodes?

Or

(b) An axially loaded stepped circular bar is having a diameter of 25mm for a

length of 300mm and a diameter of 20mm for a length of 200 mm. The

bar is fixed at left end and is subjected to an axial loaded of 60N at the

right end. Determine the element stresses and reaction force at left end.

Take E = 2 × 105 N/mm2

.

12. (a) (i) What is meant by weak formulation? Explain with an example. (8)

(ii) Derive the Lagrange linear interpolation functions for the three

noded triangular elements and sketch graphically. (8)

Or

(b) For the triangular elements having coordinates at (0,0), (2,5) and (4, 0.5)

obtain the shape functions and the intensity of pressure at a point whose

co-ordinates are (2, 1.5). The nodal values of pressures at nodes 1,2 and 3 are 60 N/m2 , 51N/m2

and 69N/m2 respectively.

13. (a) (i) Explain the Galerkin approach of deriving finite element

equations for the heat transfer problem. (10)

(ii) What are the equations to be solved in a general three dimensional

fluid flow problems? (6)

Or

(b) One dimensional element has been used to approximate the convection

distribution in a fin. the solution indicated that the temperature in node

1 and 2 are 120° and 90° respectively. Determine the temperature at

point 4cm from nodes 1 and 2 which are located at 1.5 and 6cm from the

origin.

14. (a) Explains the methods of obtaining natural frequencies of longitudinal

vibration of a stepped bar has a cross sectional area of A for length L and

2A for length L. Idealizing the bar with two elements Take A=100mm2 L=250 mm2

.

Or

(b) Explain the procedure involved in deriving the finite elements equations

of a dynamic problem. Give an example.

15. (a) Describe preprocessing, processing and post processing using any finite

elements software. Write the step-by-step procedure.

Or

(b) What is the necessity of determining Von Mises stresses in finite

elements static analysis? Explain.

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