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### FINITE ELEMENT METHODS IN MECHANICAL DESIGN ED9221 ED 9221|Model Question Paper | Previous Year Anna University Question Paper For M.E| Regulation 2009 Model Question Paper For ME Students|

Sunday, November 20, 2011 ·

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
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 step
procedure 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.