Issue 64

M. A. Kenanda et alii, Frattura ed Integrità Strutturale, 64 (2023) 266-282; DOI: 10.3221/IGF-ESIS.64.18

z/h

z/h

Figure 2: The variation of the shape functions   f z and its derivative   g z in terms of non-dimensional thickness (z/h).

The new shear deformation function is developed based on the following conditions:

h 2

z=+

f

(z)dz = 0 ; g(z)

=0 ; g(z)

=1

(3)



h 2

z=±

z=0

h 2

z=-

The linear strain field of a porous FG plate can be deduced from the displacement field in Eqn. (2) as:

  

         

2







u

θ

w

x

0

0

+ (z) f

-z

2





x

x



x

            x y z ε ε      v ε = -z  0 y

  θ

2

w

y

0

+ (z) f

(4a)

2





y

y

g'(z) θ (x,y,t)

z

  

2



θ

  

          

 

 

    0 y





u v

w

θ

y

x

0 + -2z

0

+ (z) f

+

 

x

x y

y

x

   

               xy yz xz γ γ γ

     

        z z θ y θ x  

(4b)

= g(z) θ +

y

  

g(z) θ +

x

The constitutive law is characterized by the relationship between the stress field and the strain field (Hook’s law), as:

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