Civil Engineering Reference
In-Depth Information
There are 12 equations and the skyline storage is 54
Node x-disp y-disp
1 0.0000E+00 -0.9100E-06
2 0.1950E-06 -0.9100E-06
3 0.3900E-06 -0.9100E-06
4 0.0000E+00 -0.4550E-06
5 0.1950E-06 -0.4550E-06
6 0.3900E-06 -0.4550E-06
7 0.0000E+00 0.0000E+00
8 0.1950E-06 0.0000E+00
9 0.3900E-06 0.0000E+00
The integration point (nip= 1) stresses are:
Element x-coord y-coord sig_x sig_y tau_xy
1 0.1667E+00 -0.1667E+00 0.0000E+00 -0.1000E+01 -0.8145E-16
2 0.3333E+00 -0.3333E+00 0.3331E-15 -0.1000E+01 -0.1629E-15
3 0.6667E+00 -0.1667E+00 0.1110E-15 -0.1000E+01 0.3665E-15
4 0.8333E+00 -0.3333E+00 0.4441E-15 -0.1000E+01 0.1629E-15
5 0.1667E+00 -0.6667E+00 0.2220E-15 -0.1000E+01 -0.1222E-15
6 0.3333E+00 -0.8333E+00 0.5551E-15 -0.1000E+01 -0.1425E-15
7 0.6667E+00 -0.6667E+00 0.0000E+00 -0.1000E+01 0.1833E-15
8 0.8333E+00 -0.8333E+00 0.2220E-15 -0.1000E+01 -0.4072E-16
Figure 5.5 Results from first Program 5.1 example
1
2
3
4
5
9
13
14
10
6
8
12
15
7
11
11
7
15
8
10
6
12
14
13
9
5
4
3
2
1
Freedoms numbered from 1
to
30 in same order as the nodes
Figure 5.6 Local node and freedom numbering for different orientations of 15-node
triangles
Program 5.1 is able to use both 6-node and 10-node triangular elements, but the next
member of the triangular element family to be considered is the 15-node “cubic strain”
triangle (see Appendix B). The node numbering system for all triangles involves starting
at a corner and progressing clockwise. Internal nodes, if present, (e.g. 10- and 15-noded
triangles) are numbered last. The node numbering at the element level for a 15-noded
triangle is shown in Figure 5.6. It is seen that the three internal nodes are also numbered
in a clockwise sense.
The second example and data in Figure 5.7 show half of a flexible footing resting on
a uniform elastic layer supporting a uniform pressure of 1 kN/m
2
. Because of symmetry,
only half of the layer needs to be analysed and the width has been arbitrarily terminated at
