Issue 51

S. Merdaci et alii, Frattura ed Integrità Strutturale, 51 (2020) 199-214; DOI: 10.3221/IGF-ESIS.51.16

The governing equations of equilibrium can be derived from Eqn.(10) by integrating the displacement gradients by parts and setting the coefficients δu , δv , δw b , and δw s zero separately. Thus, one can obtain the equilibrium equations associated with the present shear deformation theory,

N N u  

xy

x

 



:

0

x y N N  



y   

xy



: v

0



2 y M M M w    2 b xy

x

(15)

b

b x

2



y







q  

: b

2

0

2

2

2 y M M S S M w        2 s s s s xy y xz x y x



s

2



yz

x







   

q

:

2

0

s

2

2

 



x y 

x y





x

y

A NALYTICAL SOLUTIONS FOR FGM SANDWICH PLATE he following simply-supported boundary conditions are imposed at the side edges of the FG sandwich plate:

T





w

w

  0, v y w y w y     0,   0,

  0, y

  0, y

b

s







0

(16a)

b

s





y

y





w

w

  , v a y w a y w a y     ,   ,

  , a y

  , a y

b

s







0

(16b)

b

s





y

y

  0,

  0,

  0,

  ,

  ,

  ,

b x

s

b x

s

x x N y M y M y N a y M a y M a y       x x

0

(16c)





w

w

  , 0 u x w x w x     , 0

  , 0

  , 0 x

  x

b

s





, 0 0 

(16d)

b

s





x

x





w

w

  , u x b w x b w x b     ,   ,

  , x b

  , x b

b

s







0

(16e)

b

s





x

x

  , 0

  , 0

  , 0

  ,

  ,

  ,

b

s

b

s

y y N x M x M x N x b M x b M x b       y y y y

0

(16f)

Figure 2: Boundary conditions for full plate.

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