TO FIND DEFLECTION OF FGM BEAMS UNDER UDL

1. Project Report submitted in Fourth Year First Semester
By
ABHISHEK SAHA
BME-IV , SECTION-A
ROLL NO.-001611201032
JADAVPUR UNIVERSITY
Under the Guidance of
DR. HARERAM LOHAR
DEPARTMENT OF MECHANICAL ENGINEERING
JADAVPUR UNIVERSITY
KOLKATA-700032

2. Functionally Graded Material (FGM) belongs to a class of advanced
material characterized by variation in properties the dimension varies.
Material properties became a function of position and a continuous
variation from one surface to another can be achieved.
Functionally graded material has a large variety of applications in engineering science practice:
Engineering field (Turbine blade, helicopter blade, beams, bridges, column, shaft,
rotor)
 Aerospace field (Aerospace skins, space planes).
 Electronics field (graded band semiconductor, sensor).
Defense Field (Nuclear weapons, Missile, High Speed Jet and Rocket, Arms and
ammunitions) .

3. A lot of study have been done in the field of structural elements i.e. rod, bar,
beam, strut, column, plate, disk etc.
Different appoarch have been taken by different reseachers.
Lot of static and dynamic analysis on FGM beam are already present.
Vibration analysis have also been done by some researchers.

4. To find out the transverse deflection of the
beam at equally spaced points about the
length of the beam subjected to uniformly
distributed transverse load .

5. CASE1 :
length(L) = 1m, width(B) = 0.02m and thickness(T) = 0.005m. The beam
has E0 = 210 GPa ,ƍ0 = 7850 Kg/m3 and Poisson’s ratio(ʋ) = 0.3, where E0
and ƍ0 are the modulus of elasticity and density at the root of the beam., i.e
at x=0.
E(Ɛ) = E0(1+αɛ) and ƍ(Ɛ) = ƍ0(1+αƐ) respectively where Ɛ= x/L and value of
α are 0 and 0.5 .

6. CASE 2:
Taking the same dimension as the previous case the
Young’S modulus is varied as follows:
E(x,z) = E0*e^[0.2{(x/L)+(z/T)}]

8. VALIDATION STUDY
Alireza Khorshidi’s Beam Model :
 L=10m, T=1m, B=2m where L,B,T are the length, width and thickness
of the beam respectively. Also E0=5*106 Pa, ƍ0 = 7850 Kg/m3, ʋ = 0.3.
Beam is simply supported with UDL 1000 N/m.

9. CASE 1 :
Beam is given uniformly distributed load of 1000 N/m.

12. CASE 2:

13. From the graphs it has been observed that the CC beam has the
least deflection followed by SS beam followed by cantilever
beam.
the deflection decreases with increase in gradation factor i.e. α.
 The method may be applied to other boundary conditions and
different types of cross section as well as in the design of structures
by choosing a suitable power law the material properties can be
tailored to meet the desired goals of minimizing stress and
displacements.

14. 1. Alireza Khorshidi, Finite element analysis of a Timoshenko beam
under Prof Bower.
2. S.Tharaknath , S.govindaraji , T.anbu ,Analysis of FGM beams
under UDL load by Ritz method.
3. Sachin Sahu , Non-linear forced vibration analysis of axially
FGM beams.
4. Bendine Kouider, Satla Zouaoui ,Simulation of functionally
graded material beam with Piezoelectric Actuators.