Civil Engineering Reference
In-Depth Information
L
2
y
5
6
L
1
4
1
2
3
x
Figure 3.11 General 6-noded triangular element
6-node triangle
Another plane element available for use with the programs later in this topic is the next
member of the triangle family, namely the 6-noded triangular (
nod=6
) element as shown
in Figure 3.11.
The coordinate matrix becomes
x
1
y
1
x
2
y
2
x
3
y
3
x
4
y
4
x
5
y
5
x
6
y
6
coord
=
(3.70)
and using the same local coordinate system for triangles, the shape functions [
N
]
T
are now
(
2
L
1
−
1
)L
1
4
L
3
L
1
(
2
L
3
−
1
)L
3
4
L
2
L
3
(
2
L
2
−
fun
=
(3.71)
1
)L
2
4
L
1
L
2
Both the shape functions
fun
and the derivatives
der
are formed as usual by the
subroutines
shape_fun
and
shape_der
. The sequence of operations described by (3.47)
to (3.51) again follow to generate the stiffness matrix of the element.
3.7.9 Three-dimensional elements
Cuboidal elements
The shape functions and derivatives provided by subroutines
shape_fun
and
shape_der
allow analyses to be performed using cuboidal elements with 8, 14, or 20 nodes (see
Appendix B).
