PSI - Issue 26

Merdaci Slimane et al. / Procedia Structural Integrity 26 (2020) 35–45 Slimane et al. / Structural Integrity Procedia 00 (2020) 000 – 000

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3

becomes to an imperfect FG plate due to the effect of even porosities in its material properties distribution. The material properties of the plate FG, such as Young’s modulus E, are assumed to be function of the volume fraction of constituent materials. The function of the P-FGM power law is commonly used to describe these variations in the properties of materials.

Fig. 1. Geometric configuration of FG plate with porosity in the rectangular Cartesian coordinates.

Fig. 2. Even porosity distribution through the cross-section area of P-FGP.

Assume that the FG plate is made of a mixture of metal and ceramic. It is manifest that the material properties of the FG plate (i.e., Young’s modulus E , Poisson’s ratio ν , and mass density ρ ) are changed continuously with the material composition in the thickness direction. The bottom surface of the rectangular plate is assumed to be metal and the top surface is made of ceramic. Furthermore, the influence of porosities, which may exist inside the materials of FG plate during the production, is included. By expanding Eq. (1), the material properties of imperfect FG plate with even porosities (the plan of this model is shown in Fig.2) can be rewritten as follow Belabed et al. (2014).

p

ξ 2

1 z 2 h

  

  

(1a)

(

)

(

)

E z E E ( ) = −

E E E + + − +

c

m

m

c

m

p

ξ 2

1 z 2 h

  

  

(1b)

(

)

(

)

υ z υ υ ( ) = −

υ υ υ + + − +

c

m

m

c

m

p

ξ 2

1 z 2 h

  

  

(

)

(

)

(1c)

ρ z ρ ρ ( ) = −

ρ ρ ρ + + − +

c

m

m

c

m

In which subscripts of E c and E m represent the material properties of ceramic and metal, respectively. Also, “P” is the volume fraction index (power-law) that defines the material variation characterization through the thickness of the plate, and ξ (0 ≤ ξ ≤ 1) shows the porosity volume fraction.

3. Assumptions of the HSDPT are as follows

The higher-order shear deformation plate theory (HSDPT) theory takes into account transverse shear strain in the formulation with the following assumptions.