PSI - Issue 26

Merazi Mohamed et al. / Procedia Structural Integrity 26 (2020) 129–138 Merazi et al. / Structural Integrity Procedia 00 (2020) 000 – 000

135

7

Further, the transverse load q is also expanded in double Fourier series as

b n y 



( )   =  = = 1 1 , m n q x y

sin a q m x mn

(21)

sin

For the case of a sinusoidally distributed load, we have m n 1 = = and 0 11 q q =

(22)

Where 0 q represents the intensity of the load at the plate centre. Eqs. (20), (21) and equation (22) reduce the governing equations to the following form       C P  =

(23)

Where

   T f



   T U , V , W , W  =

 smn

mn 0,0, q , q =

and

mn

mn

bmn

mn

Where [C] refers to the flexural stiffness.

4. Numerical results

The study has been focused on the static behavior of functionally graded plate based on the present new hyperbolic shear deformation plate theory and based on neutral surface position. A functionally graded material consisting of Aluminum - Alumina is considered. The following material properties are used in computing the numerical values.

Table 1. Material properties of FGM constituents. Material

Poisson’s Ratio, ν

Elasticity modulus, E[GPa]

Metal (Aluminum, Al) Ceramic (Alumina, Al 2 O 3 )

E m = 70 E c = 380

0.3 0.3

Figure 3 shows the variation of non-dimensionalised central deflection of a square plate with power law index n.

Fig. 3. Non dimensionalised central deflection w versus power low index n for a simply Supported square FGM plate under sinusoidal load.