Page 73 - Finite Element Analysis with ANSYS Workbench

64 Chapter 4 Plan Stress Analysis

3 3

4
5
2 2
6
1 1
3 7 3
4 4
6
8
2 2
1 1 5

The three-node triangular element is the simplest two-
dimensional element to understand. Both u and v displacements
are assumed to vary as flat planes over the element as shown in the
figure.
ux y
(, )

(, )
vx y 3
u 2
v
2 2
Displacement
t
y
1
x

(, ) 
ux y N 1 (, )yu  x 1 N 2 ( , )yu  x 2 N 3 (, )yu
x
3
(, ) 
vx y N 1 (, )yv  x 1 N 2 ( , )yv  x 2 N 3 (, )yv
x
3
where N N N are the element interpolation functions,
,
,
2
3
1
1
)a 
(, ) 
Nx y ( b x  c y i  1, 2, 3
i
2A i i i
and A is the element area,