PPT on laminated composite

1. ANALYTICAL INVESTIGATIONS ON
LAMINATED COMPOSITE USING
REFINED THEORIES
A Presentation By:
S.M.Ghumare
Department of Civil Engineering
Sanjivani College Of Engineering
Kopargaon, (M. S.) India

2. Introduction to Composite
 The fiber or particle embedded in matrix of another material are
the best example of modern day composite material, which is
most structural.
 Now a days, the matrix based structural composite material is
widely accepted because of –
Weight advantage, Moisture sensitivity,
Good electrical resistivity, Resist variation in temperature,
Easy Handling, High specific strength and stiffness,
Less shrinkage, Corrosion resistant and so many

3. Uses of Composite Material
 Wide spread use of these shear flexible material is
as follows-
Aircraft
Automotives
Shipbuilding
Roof covering
Panels

4. Introduction to theory
 The numerous plate theories that have been developed since the
late 19th century
 Most commonly used and widely accepted theories are
i)Kirchhoff theory of plates (CPT)
ii)Mindlin–Reissner theory of plates (FSDT).
 The shear deformation effects are more pronounced in thick plates
These effects are neglected in CPT.

5. Introduction to theory
Now a days, the use of laminated composites in thin walled
structure increased, hence the effect of transverse shear deformation
can not be neglected.
In order to describe the correct bending behavior of thick plates
including shear deformation effects and the associated cross sectional
warping, shear deformation theories are required.
This can be accomplished by selection of proper kinematic and
constitutive models.

6. Introductions of Basic Theories
( , )
( , ) ( )
dw
u x z z
dx
w x z w x
= −
=
 CPT: In the CPT, it is assumed that plane sections initially normal to the
mid surface before deformation remain plane and normal to that surface
after deformation. This is the result of neglecting transverse shear
strains.
 The CPT derived from Kirchhoff's hypothesis ignores the transverse
shear strains / stresses in the plate..
 As CPT does not take into account shear effects, hence many theories
got evolved to address the deficiency.

7. Introduction of Refined Theories
 Mindlin plate theory- Modification over CPT
FSDT is based on hypothesis that the plane section which is perpendicular
to the neutral plane before bending remains plane but not necessarily
perpendicular to the neutral
plane after bending.
 In FSDT, Shear strain is constant through the thickness and also it
requires shear correction factor which is problem dependent.
 To remove the discrepancies in the CPT and FSDT higher order theories
were developed for the static and vibration analyses of beams.
( ), ( )
( , ) ( )
u x z z x
w x z w x
φ= −
=

8. Introductions of Refined Theories
 Trigonometric shear deformation theory
It takes into account transverse shear deformation effect as well
as transverse normal strain effect for cylindrical bending of thick
orthotropic plates.
( , ) sin
( , ) ( )
dw h z
u x z z
dx h
w x z w x
π
φ
π
 
= − +  ÷
 
=

9. Introductions of Refined Theories
•Hyperbolic Shear Deformation Theory
Contains hyperbolic function
•Accurate results and superior over other theories
•Gives hyperbolic variation of transverse shear stress over
thickness
1
( , ) cosh sinh
2
( , ) ( )
w z
u x z z z h
x h
w x z w x
φ
∂     
= − + − ÷  ÷ ∂     
=

10. Introductions of Refined Theories
•Second order shear deformation theory
(SSDT)
•Higher order shear deformation theory
(HSDT)
• Exponential (ESDT) shear deformation theory

11. Author Theory Displacement field Description
Euler Bernoulli ETB Based on assumption that plane sections
which are perpendicular to neutral axis
before bending remain plane after
bending
Timoshenko FSDT
[1]
Proposed to overcome the limitation of
ETB, by accounting transverse shear
effect.
Levinson,
Reddy
HSDT
[2,3]
Developed to avoid the use of shear
correction factor and have a better
prediction of response of composite
beams.
M.Levy,
Touratier,
TSDT
[4]
Flexural analysis of beam which
satisfies the shear stress free condition
at top and bottom surfaces of the beam.
( ) ,
( ) ( )
dw
u x z
dx
w x w x
=−
=
( ) ( ),
( ) ( )
u x z x
w x w x
φ=−
=
( )
2
( ) ( ) ,
( ) ( )
4
where, 1
3
dw dw
u x z f z x
dx dx
w x w x
z
z
h
φ
 
= − + + ÷
 
=
  
−  ÷
   
( ) sin ( ),
( ) ( )
dw h z
u x z x
dx h
w x w x
π
φ
π
 
= − +  ÷
 
=
REVIEW OF LITERATURE

12. Author Theory Displacement field Description
Sayyad and Ghugal
[5]
TSDT Includes effect of transverse
normal strain.
Soldato , Ghugal
and Sharma [6]
HSDT Used for the static and dynamic
analysis of thick isotropic
beams.
Sayyad [7] USDT Carried out comparison of
various shear deformation
theories for free vibration and
bending analysis of thick
isotropic beam.
Sayyad and Ghugal
[8]
USDT Carried out comparison of
various shear deformation
theories for free vibration and
bending analysis of thick
isotropic beam considering
combined effect of shear
bending and shear slope.
0
( ) sin ( )
( ) cos
dw h z
u x z x
dx h
h z
w x w
h
π
φ
π
π
ξ
π
 
=− +  ÷
 
 
= +  ÷
 
1
( ) cosh sinh ( )
2
( ) ( )
dw z
u x z z h x
dx h
w x w x
φ
    
= − + − ÷  ÷ 
    
=
( ) ( ) ( ),
( ) ( )
dw
u x z f z x
dx
w x w x
φ= − +
=
( )( ) ,
( ) ( )
dw dw
u x z f z
dx dx
w x w x
φ
 
= − + + ÷
 
=

13. Necessity of Refined Theories
 The shear deformation effects are more pronounced in
thick plates when subjected to transverse loads than in
thin plates under similar loading.
 In order to describe the correct bending behavior of thick
plates including shear deformation effects and the
associated cross sectional warping, shear deformation
theories are required.
 To carry out one dimensional analysis of laminated plates

14. Objectives of the Study
 The main objective of this study is to develop a new refined
theories for the laminated composites.
 To formulate a simple yet accurate trigonometric shear
deformation theory for the analysis of laminated beams and plates
which takes into account effect of transverse normal strain.
 To establish the credibility of these theories by applying them to
static flexure of laminated beams and plates.
 To obtain results for the simply supported laminated beams and
plates subjected to various loading cases which are rarely
available in the literature.

15. Scope in the Research Area
• In this area more emphasis should be given for the
assessment of various displacements based shear
deformation theories for the analysis of laminated beams
and plates
•Combine effect of bending and shear rotation can be
assessed using higher order theories and theory of elasticity.
•The flexure of laminated beams and plates subjected to
parabolic loading and linearly varying load can be studied
which not been available in the literature

16. List of Publication
•Ghumare S.M. and Sayyad A. S., “Cylindrical Bending Of
Composite Plates Using Refined Plate Theory” International Journal
of Advanced Technology in Civil Engg.,ISSN2231-5721,Volume
-2,Issue,2013
•Ghumare S.M. and Sayyad A. S “Assessment Of Refined Beam
Theories For The Bending Analysis Of Composite Beam”
International Journal of Advanced Technology in Civil
Engg.,ISSN2231-5721,Volume -2,Issue,2013
• Sayyad A. S., Ghumare S.M. and Sasane S.T. “Cylindrical Bending
Of Orthotropic Plate Strip Based on nth-Order plate theory” Journal
of Materials and Engineering Structures ,Mouloud Mammeri
University of Tizi-Ouzou ,Algeria ( Revived Paper )

17. References
1. R. P. Shimpi and H. G. Patel, “A two variable plate theory for
orthotropic plate analysis,” International Journal of Solids and
Structures, vol. 43, 2006, pp.6783–6799
2. J. N. Reddy, “A general non-linear third order theory of plates with
moderate thickness,” International Journal of Non-linear Mechanics
25, vol.6, 1990, pp.677-686.
3. Y. M. Ghugal, R. P. Shimpi, “A review of refined shear
deformation theories for isotropic and anisotropic laminated
beams,” Journal of Reinforced Plastics and Composites, vol.21,
2002, pp.775-813.

18. •E. I. Starovoytov, E. P. Dorovskaya, and S. A. Starovoytov,
“Cylindrical Bending Of An Elastic Rectangular Sandwich Plate On
A Deformable Foundation”Mechanics of Composite Materials, Vol.
46, 2010,pp.95-140
•Reddy J. N. and Robbins D. H., “Theories and Computational
Models for Composite Laminates”, ASME Applied Mechanics
Reviews, 1994, 47, pp. 147-169
•Pagano N. J., “Exact Solutions for Bidirectional Composites and
Sandwich Plates”, Journal of Composite Material, 1970, 4, pp. 20-
34.
References

19. THANK YOU