Page 47 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

34 • Using ansys for finite element analysis
1.8 examPles of linear fem

Example 1
For the structure shown in the figure, determine the nodal displacements,
the forces in each element, and the reactions.

2 3
2
1 1 2 3 15 kN 4 E = 210 GPa
–4
3 m A = 3 × 10 m 2
4 5
2
3 m

EA
k = thestiffnessofelement
L

All elements of the previous figure have the same material and
dimensions.


EA 1 − 1
k () = k () = k () = k () = k =  
2
4
3
1
L − 1 1 

3  1 −  1
*
k = 210 10 * 300  
3000  −1 1 
21
 21 − 
k =   * 10 3
 −21 21 
The global stiffness matrix (K)

K = k + k + k + k 4
2
3
1
  21 −21 000   0 0 0 0 0  0 0 0 0 0  0 0 00 0 
0
  −21 21 000   0 21 − 210 0   0 21 0 − 21 0   0 21 0 0 − 21 
        

3
K = 10 *  0 0 000  + 0 − 21 21 0 0 + 0  0 0 0 0 0 +  0 0 00 0 
        
  0 0 000   0 0 0 0 0   0 − 210 0 0   0 0 00 0 

    0 0 000   0 0 0 0 0   0 0 0 0 0   0 0 − 210 0 21 
 
 
 