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Register Number: ..

M.E. DEGREE EXAMINATIONS: JUNE 2014

(Regulation 2013)

Second Semester

CAD/CAM

P13CCT202/CCM502: Advanced Finite Element Analysis

Time: Three Hours Maximum Marks: 100

Answer all the Questions:-

PART A (10 x 2 = 20 Marks)

1. Analyse the figure given below and conclude what will be the size of the stiffness matrix if you

choose it has linear 1-D element having two degrees of freedom at each node.

2. Outline the properties of stiffness matrix.

3. Differentiate between CST element and LST element with diagram.

4. Distinguish plane stress and plane strain analysis with suitable examples.

5. List the types of non-linearity.

6. Draw any two axi symmetric element.

7. Define static condensation?

8. Why do we use Numerical integration in FEM?

9. How mass matrix differs from the stiffness matrix?

10. How many natural frequencies and mode shapes does a distributed mass system will have?

Answer any FIVE Questions:-

PART B (5 x 16 = 80 Marks)

Q.No:11 is Compulsory

11. Derive the stiffness matrix and its finite element equation for a beam element

12. Evaluate the element stiffness matrix for the elements shown in figure below.

The coordinates are given in mm. Assume plane stress conditions. (Ap)

Take E = 210 GPa

= 0.25 and t =10 mm.

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(15,5)

(15,10)

(10,7.5)

13. Formulate the element stiffness matrix of an axisymmetric triangular element

14. (i) What are the advantages of Gaussian quadrature numerical integration for

isoparametric elements? (6)

(ii) Evaluate the integral, l = [ ]dx

xxe x

213 2

1

1 +++

using one point and

two point gauss-quadrature. Compare this with exact solution.

(10)

15. Develop the element stiffness matrix and mass matrix for a rod under free axial

vibration.

16. Find the natural frequencies of longitudinal vibrations of the stepped shaft of

areas A and 2A of equal lengths (L), when it is constrained at one end, as

Shown below.

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