Lovely Professional University 2012 M.Tech Mechanical Engineering Finite element method MEC-912 - Question Paper
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ROLL NO.: SECTION: M2116 |
TEST-1 FINITE ELEMENT METHODS (MEC912) TIME: 45mins FULL MARKS-20 |
(1) A simply supported beam of uniform cross section and length L is loaded by a central concentrated load, P. Assume that the beam deflects into the sine wave as shown in fig
/ Jtx\
below, such that y = A sin ( 1 . This assumed shape is a trial function and A is an undetermined coefficient.
Since the elastic strain energy due to bending is given by: U = ~J El (d2 y / dx2 ) dx. Determine the displacement at the centre of the beam using Rayleigh-Ritz method. The symbols have their usual meaning. [8]
(2) A displacement field: u = 1 + 3 x + 4x 3 + 6 xy2 ;
v = xy lx2
is imposed on the square element as shown in fig below:
y
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(1,1) | ||
(-1.-1)
(a) Write down the expressions for: ex , ey and yxy.
(b) Find where ex is maximum within the square. [4]
(3) A long rod is subjected to loading and a temperature increase of 30oC. The total strain at a point is measured to be 1.2 X 10-5. If E = 200 GPa and a = 12 X 10-6/oC, determine the stress at the point. [4]
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(4)Determine the displacements of nodes of the spring system shown in fig below: |
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[4]
(1)
ACADEMIC TASK -3 TEST-2
FINITE ELEMENT METHODS (MEC912)
ROLL NO.:
SECTION: M2116
TIME: 45mins FULL MARKS-20
For the axisymmetric triangular element shown in figure below, determine the element strain [er ez yrz ee]T and element stress [or oz Trz oe]T. Take E=2.1x105 N/mm1 and u= 0.25. The co - ordinates are in mm. The nodal displacements are 1=0.05mm, wO.OBmm, u2=0.02mm, w2=0.02mm, u3=0.0mm, w3=0.0mm.
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The strain-displacement matrix is given by: 23 | |||||||||||||||||||||||||||||||||
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det J 0 hi det J M r |
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and the stress-strain matrix is given by: |
 |
B =
[8]
It is divided into two CST elements. Determine the nodal displacement and element stresses using plane stress conditions. Body force is neglected in comparison with the external forces.
Take, Thickness (t) = 10mm,
Young's modulus (E) = 2x105 N/mm2,
Poisson's ratio (v) = 0.25.
[6]
(3)
A unidirectionally-reinforced glass-epoxy lamina shown below has the following properties: E1 = 53 GPa, E2 = 18 GPa, v 12 = 0.25, G12 = 9 GPa. The load P is applied in the 1-direction. Note: This lamina is orthotropic.
[4]
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Determine strains 1 and s2 under the force P. |
0.1 mm before the load is applied
Wood is an orthotropic material. Comment
(4)
[2]
A two dimensional propped beam is shown in figure below:
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Attachment: |
| Earning: Approval pending. |
