Civil Engineering Reference
In-Depth Information
Read data
Allocate arrays
Find problem size
Null global stiffness matrix
For all elements
Find nodal coordinates and steering vector.
For all integrating points
Compute shape functions and derivatives in
local coordinates.
Convert from local to global coordinates.
Form the product [B]
T
[D][B] and add contribution
into element stiffness.
Assemble element stiffness matrix into global system.
Factorise the global stiffness matrix.
Read the loads and/or displacements.
Complete equation solution.
For all elements
Find nodal coordinates and steering vector.
Retrieve element nodal coordinates.
Retrieve element nodal displacements.
For all integrating points
Compute shape functions and derivatives in
local coordinates.
Convert from local to global coordinates.
Form the [B] matrix.
Compute the strains and stresses.
Figure 5.1 Structure chart for all Chapter 5 programs involving assembly
generated by subroutine
geom rect
assumes that all elements are right-angled, congruent
and formed by diagonal lines drawn from the bottom left corner to the top right corner of
the surrounding rectangles. Figure 5.3 shows the node and element numbering for this case
assuming
dir = 'x'
. Figure 5.4 shows the order of node and freedom numbering at the
element level. Node 1 can be any corner, but subsequent corners and freedoms must follow
in a clockwise sense. Thus, the top left element (
iel=1
) in Figure 5.2 has a steering vector
g
=
[ 780623]
T
.
It is expected that, where necessary, users will replace the geometry subroutine
geom
rect
by more sophisticated versions. It need only be ensured that the coordinates and
node numbers are generated consistently.
Referring to Figure 5.2, the first line of data reads the type of strain conditions
type
2d='plane'
, thus a plane-strain analysis is to be performed. The next line reads
ele-
ment='triangle'
,
nod=3
,and
dir='x'
, which indicates that 3-noded triangles will
be used with node and element numbering in the
x
-direction. The next line reads
nxe=2
,
[ 012306]
T
and its neighbour (
iel=2
) has a steering vector
g
=
