Page 25 - Finite Element Analysis with ANSYS Workbench

16 Chapter 2 Truss Analysis

u 1 u 2

F F
1
1 A, E 2 2
x
L

The displacement distribution is assumed to vary
linearly along the element axial x-direction in the form,
 u 1 
()  Nx u 
ux 1 () 1 N 2 ( ) u  Nx 2 ()   x   
x
() N

2
1
u

2
 N ()   x   
u



(1 2) (2 1)

ux u 2 where Nx and Nx are the
()
()
()
2
1
element interpolation functions.
For this two-node element, they
u 1 are,
x
()
1 2 Nx  1
1
L
x
L and Nx  x
()
2
L

A truss element may contain more than two nodes.
As an example, the three-node truss element, as shown in the
figure, assumes the displacement distribution in the form,
()
ux u 3 ux N 1 () u  N 2 ( ) u 2
() 
x
x
1
 Nx 3
() u
3
u 1 u 2  u 1 
 
x
x
u

 Nx N 2 () N 3 ()  
()
2  

1
1 3  
u

x L 2 L  N ()   x    3

u


2 2 (1 3) (3 1)
where Nx , Nx 3 ()
()
() และ Nx are the interpolation functions
2
1
expressed by,