Civil Engineering Reference
In-Depth Information
Exterior boundary surface
Surface
normals
Ω
Opening
Opening
Opening
Interior boundary surfaces
Figure 2.5
Boundary of a 3D domain.
2.3.10.4 Node labelling of FEs
A corner point of a geometrical object such as a triangle or a cube is called a vertex, and
nodes of an FE are at the vertices; sometimes additional nodes for higher-order elements can
be placed at the mid-point of an edge, at a face or even at the centre of an element. However,
in linear p1 FE meshes, the nodes and vertices of an element are identical in number and in
their positions, and hence, when there is no confusion, either one can be used to refer to a
corner point of an element.
i.
Triangular and quadrilateral elements
The nodes of a triangular or quadrilateral element on 2D domains are labelled in a
counter-clockwise manner, as shown in Figures 2.2 and 2.3, and on a spatial surface,
the nodes of a triangular or quadrilateral element are labelled according to the orienta-
tion of the surface. A triangular mesh
or a quadrilateral mesh
of N
E
elements can
be stored in a linear array:
{
}
{
}
a
a
T
=
Va
,
=
123
, ,
andi
=
1
,
N
,
Q
=
V
,
a
=
1 234
,,,
and i
=
1N
E
,
i
E
i
ii.
Tetrahedral, hexahedral, pentahedral and pyramid elements
Nodes on a face of the tetrahedral element or on the quadrilateral base of the pyramid
element are labelled following the right-hand grip rule pointing towards the apex, as
shown in Figure 2.6a and 2.6d. Nodes of a hexahedral or a pentahedral element are
labelled in two layers in an order following the right-hand grip rule pointing towards
the second layer, as shown in Figure 2.6b and 2.6c. A tetrahedral mesh
, a hexahe-
dral mesh
, a pentahedral mesh
or a pyramid mesh
of N
E
elements can be stored
sequentially in a linear array, i.e.
{
}
{
}
a
a
T
=
Va
,
=
14
,
andi
=
1
,
N
,
H
=
V
,
a
=
1 8
,
and i
=
1
,
N
i
E
i
E
{
}
{
}
a
a
P
=
Va
,
=
16
,
andi
=
1
,
N
,
Y
=
V
,
a
=
1 5
,
and i
=
1
,
N
i
E
i
E
