Page 131 - Finite Element Analysis with ANSYS Workbench

122 Chapter 7 Vibration Analysis

 2 w
  Ez
x  2

2D Plate
,
The stress components    of the plate are
,
xy
x
y
determined at any z coordinate from the computed deflection w
as,
E   2 w  2 w 
       z
x
1    2 x  2 y  2 
E   2 w  2 w 
       z
y
1    2 x  2 y  2 
E   2 w 
 xy    z
1     xy  

3D Solid

,
The three normal stress components    and
,
y
x
z
three shearing stress components  xy , xz ,  are determined from
yz
,
the computed displacement components ,u v w as,
E   u v   w 
   (1   )     
x
(1   )(1 2 )    x  y  z  
E   u v   w 
     (1   )   
y
(1   )(1 2 )    x  y  z  
E  u v   w 
 z  (1   )(1 2 )      x    y   (1   ) z   
E   u v  
    
xy
2(1    )  y x  
E   u  w 
    
xz
2(1    )  z x  
E  v   w 
    
yz
2(1    )  z y  