Computational Fluid Structure Interaction - Computational Hemodynamics: Theory, Modelling and Applications - page 133

Fig. 5.38 Nodal displace-
ment and forces occurring for
a 2D triangular element

where the solution is

u = 0.133m, u = 0.167m, and FN = 4

2 3 1

Two-Dimensional Finite Element Example We now consider a 2D triangular ele-
ment with three nodes subjected to plane stress (no displacement in the z -coordi-
nate) (Fig. 5.38 ).
The element has three nodes in the x-y coordinate, with each node having two
degrees of freedom movement in x , and y directions). Displacements at some point
inside a finite element { u } can be determined with the use of nodal displacements
{ d } and shape functions N i . Nodal displacements in the x -coordinate direction are
u 1 , u 2 , and u 3 , while displacements in the y direction are v 1 , v 2 , and v 3 .

uxyNxyuNxyuNxyu (, ) = ( ,) + (, ) + ( ,) [ {} = N u

1 1 2 2 3 3

(5.69)

vxyNxyv (, ) = ( ,) + Nxyv Nxyv (, ) + ( ,) [ {} = N v

1 1 2 2 3 3

and in matrix form is:

u
v
u
v
v
u
v

1

1

2

u
v

N 0 N 0 N 0

=

1 2 3

→ uNd

1

0 N 0 N 0 N

1 2 3

2

3

3