Ed 9221 — Finite Element Methods in Mechanical Design

Reg. No. :

M.E. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010

Second Semester

Engineering Design

ED 9221 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. What are nonconforming elements? Name one problem where it is applied.

2. State the importance of patch test.

3. How is discretization done by quadtree method?

4. Write down the Shape function of a one-dimensional line element with two

nodes.

5. What is mapping of elements?

6. Compare: Consistent and lumped mass matrix.

7. What is constant strain element?

8. Draw an Eight noded shell element.

9. Give some practical examples of plasticity computation.

10. State a few modelling considerations in non-linear FE Analysis.

Question Paper Code : 97767

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PART B (5 16 = 80 Marks)

11. (a) Find the stresses induced in the axially loaded stepped bar shown in

Figure 1. The bar has cross = sectional areas of ( )1A and ( )2A over the

lengths ( )1l and ( )2l respectively. Assume the following data : ( )1A = 2 cm2

( )2A =1 cm2 ; ( )1l = ( )2l =10 cm ; ( ) ( ) 721 102=== EEE N/cm 2 13 =p N.

Figure. 1

Or

(b) What is a convergence criterion? Using Finite Element methods obtain a

sequence of approximate solutions as the element size is reduced

successively.

12. (a) Find the approximate deflection of a simply supported beam under a

uniformly distributed load p (Figure 2) using the Rayleigh = Ritz method.

Figure. 2

Or

p per unit length

l x

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(b) Derive the coordinate transformation matrix for the one dimensional

element shown in Figure 3, where iq and iQ denote, respectively, the

local ( )yx, and the global ( )YX , nodal displacements of the element.

Figure. 3

13. (a) Find the stresses in the plate shown in Figure 4 using one triangular

membrane element.

E = 205 GPa, = 0.3, t = 10mm

Figure. 4

Or

4q 4Q

3q

3Q

2q 2Q

1q

1Q

i

j

x

X

y Y

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(b) Find the steady state temperature distribution in the one-dimensional fin

shown in Figure 5 considering both convection and radiation losses from

its perimeter surface. Assume = 0.1 and = 5.7 108 W/cm2K4.

Figure. 5

14. (a) Find the natural frequencies and modes of vibration for the one-element

cantilever beam.

Or

(b) Derive the dynamic equation of motion for FEA.

15. (a) Derive the general formulation of strains for Von Mises theory.

Or

(b) Explain Geometric non-linearity with suitable example.

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Ed 9221 — Finite Element Methods in Mechanical Design

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