Page 51 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

38 • Using ansys for finite element analysis
Where: [R ]= [R] when derived with β .
j
i
i=3
K [] = ∑ k i () i = 12 3
,,
i=1
And, the next steps as the same in example 1.

Example 3
Analyze a thin plate of uniform thickness t = 5 mm using an appropriate
finite element formulated in part (a) and (b). The recommended mesh
for the plate is shown in the figure. Determine the displacement at point
(250, 125) and stresses in the element A only. Use E = 210 GPa and
ʋ = 0.30.

4 3
(4)
(1), A 5 (3) 250 mm

(2)
1 2

500 mm 30°
(a) 40 kN

The governing global matrix equation is:
{F} = [K]{d}
Expanding matrices in global matrix equation, we obtain

 F   R x 1  d   0 
x 1
x 1
 F   R   d   
 1 y   1 y    1 y   0 
 F x   20000   d x  d 
 2     2   2 x 
d
d
y
y
 F 2 y   34641   2   2 
 F   R   d   
x
 3 x   3 x  K  3  K  0 
 F  =  R  =[] d  =[] 
 3 y   3 y   3 y    0 
 F 4 x    R 4 x   d 4 x   0 
       
y
 F   R 4 y   d 4 y   0 
4
 F   0   d   d 5 x 
 5 x     5 x   
y
 F   0   d   d 
 5 y      5 y   5 