Issue 55

S. Merdaci et alii, Frattura ed Integrità Strutturale, 55 (2021) 65-75; DOI: 10.3221/IGF-ESIS.55.05

The FGM plate is subjected to a transverse load q(x, y) for deformation analysis of the plate and a rectangular cartesian X and Y co-ordinates are attached. The analysed plate is bounded by coordination levels ( x = 0, a ) and ( y = 0, b ). Let the present platform be transformed by exponential or polynomial law from lower to upper surfaces .First and foremost, we will look at a non-homogeneity material with a porosity volumetric function, namely, ξ (0 ≤ ξ ≤ 1). The functional relation for the ceramic and metal FGM plates between E(z) is assumed.

p

 

z h

1 2

  

  







  E z E E ( )

   

E E E

(1)

c

m

m

c

m

2

When E c and E m are the corresponding ceramic and metal elements, and " P " is an exponent volume fraction that takes values greater or equal to zero. The above power law theory demonstrates a simple blending rule used to achieve the efficient characteristics of a ceramic metal platform. The theory of shear deformation plates is ideal for displacements in this study:





w

w

      b b x w y 

s

 u x y z u x y z ( , , ) ( , )

f z

( )

0



x



w

s

 v x y z v x y z ( , , ) ( , )

(2)

f z

( )

0



y

 w x y z w x y w x y  ( , , ) ( , ) ( , )

b

s

In the present theory, this function f(z) is considered:

         2 z h h

 

( ) f z z

z

sin

(3)

With the small strain assumptions, the strain-displacement relation is given by the following equation:

b x

s

b

s

0

0

(4a)

 

  

 

  

 z



z k f z k

z k f z k

( ) ,

( ) ,

0

x

x

x y

y

y

y

b

s

s

 s

0

  xy

  





  , yz



(4b)

z k f z k

g z

g z

( ) , xy

( )

( )

xy

xy

yz

xz

xz





   

 

   

   

2

2





w

w



u

  b

s

0

2

2





x

x

                                  , , ( ) 1 s s yz s s xz y g z w x      w

                       , b x b y b xy k k k

 

      0                0 0 y xy    x

    s x k

x

2

2





v

w

w

df z

( )

                  , s y s xy k k 

b

s

0

 

(5)

2

2

y

dz





y

y

       0 0 u v y x

2

2





w

w

  

  

  

b

s



2

2

 

 

x y

x y





The constituent relationships can be written as elastic and isotropic FGMs

            x y xy 

        , x yz         y xy     zx 

11 Q Q Q Q 12

0 0

    

    

12

        yz zx

Q

0

  

  

44





(6)

22

Q

0

55

Q

0 0

66

Using the material properties, the coefficients of stiffness, Qij , can be expressed

67