Register Number
SATHYABAMA UNIVERSITY
(Established under section 3 of UGC Act,1956)
Course & Branch :B.E - AERO
Title of the Paper :Finite Element Methods
Sub. Code :AEE01 (2008)
Date :16/11/2012
Max. Marks:80
Time : 3 Hours
Session :AN
_______________________________________________________________________________________________________________________________
1.
PART - A
(10 x 2 = 20)
Answer ALL the Questions
What is meant by Finite Element Analysis?
2.
What are ‘h’ and ‘p’ versions of Finite Element Method?
3.
Draw the shape function variation for a 3-noded 1D element.
4.
With Neat sketch derive the Transformation matrix between
Element Local Displacements to Global Displacements.
5.
Write down the Constitutive Relationship for Plane Stress Case.
6.
With clear formulation, explain the need of Jacobian Matrix.
1
7.
Using two point Gaussian quadrature formula solve  e dx.
x
1
8.
What are the conditions for the problem to be Axi-symmetric?
9.
Name any 4 FEA software.
10. Consider a two noded bar of length 75mm and the nodal
temperature at node 1 and 2 are 323k and 233k. Find out the
temperature at 30mm from node 1.
PART – B
(5 x 12 = 60)
Answer ALL the Questions
11. Explain the convergence criteria of finite element method.
The differential equation of a physical phenomenon is given by
d2y
 500x 2  0
dx2
0  x  1.
By using the suitable trail function, calculate the values of the
unknown parameters a1 and a2 by using Galerkin method.
(or)
12. A beam of length 10 m, fixed at one end and supported by a
roller at the other end carries a 20 kN concentrated load at the
centre of the span. By taking the modulus of elasticity of material
as 200 GPa and moment of inertia as 24 x 10-6 m4, determine:
(a) Deflection under load
(5)
(b) Shear force and bending moment at mid span. (6)
(c) Reactions at supports
(5)
13. Determine the nodal displacements and element stress by finite
element formulation for the following figure.
(Hint: The structure is divided in to three elements)
(or)
14. Figure shows a two-member plane truss supported by a linearly
elastic spring. The truss members are of a solid circular cross
section having d = 20 mm and E = 80 GPa. The linear spring has
stiffness constant 50 N/mm.
15. The (x,y) co-ordinates of a node 1,2 and 3 of a triangular element
are given by (0,0), (3,0), (1.5,4) mm respectively. Obtain Strain
Displacement Matrix [B]. Also find N1,N2 and N3 at an interior
point P(2,2.5) mm for the element.
(or)
16. For the Axisymmetric element having a nodal Coordinates of
note {0,0}, node 2{50,0}, node 3{0,50}. Determine the elemental
stresses. Let E = 210GPa and v = 0.25. The nodal displacements
are given by {u1,u2,u3} = {0.05, 0.02,0} and {w1,w2,w3} =
{0.03, 0.02, 0}.
Hint: All Dimensions are in mm
17. With the help of appropriate sketch, make a step by step
procedure for solving 3D structure using FEM.
(or)
18. Derive the Shape function for 9 noded Rectangular element in
Natural Coordinate system.
19. Using Gauss Elimination
simultaneous equation.
3x + 4y – z = 3
x – 2y + 9z = 8
2x – 8y + z = -5
method,
solve
the
following
(or)
20. Determine steady state temperature distribution in the rectangular
fin having 120mm long and 160mm wide and 1.5mm thick. The
inside wall is at a temperature of 330C. The ambient air
temperature is 30C. Assume K = 0.2 W/mmc and h = 2e –
4W/mm2C.