Description
For this project you will be solving the Truss Topology problem via Linear Programming (LP).
This should be a single Matlab script called \My Truss Lastname.m” (where Lastname is replaced by your last name)
The possible link locations is an 11 20 (assume meters) grid shown in Figure 1
Note the node with the red arrow, n Figure 1, is the location of the load ( = 4 units of force) that your system has to support.
We assume that the truss members have an area equal to 1 and the yield strength is equal to 8.
10
8
6
4
2
0
0 5 10 15 20
Figure 1: This gure shows the three anchors along with the grid of possible link connects (which are xed) and the load location
plot([19 19],[5 3],’r’,’Linewidth’,2) plot([19 18.5],[3 3.5],’r’,’Linewidth’,2) plot([19 19.5],[3 3.5],’r’,’Linewidth’,2) plot([0 -1 -1 0],[6 5.7 6.5 6],’k’,’Linewidth’,2)
1
plot([0 -1 -1 0],[5 4.7 5.5 5],’k’,’Linewidth’,2) plot([0 -1 -1 0],[4 3.7 4.5 4],’k’,’Linewidth’,2) plot([-1.5 -1],[3.5 3.8],’k’,’Linewidth’,2) plot([-1.5 -1],[3.8 4.1],’k’,’Linewidth’,2) plot([-1.5 -1],[4.1 4.4],’k’,’Linewidth’,2) plot([-1.5 -1],[4.5 4.8],’k’,’Linewidth’,2) plot([-1.5 -1],[4.8 5.1],’k’,’Linewidth’,2) plot([-1.5 -1],[5.1 5.4],’k’,’Linewidth’,2) plot([-1.5 -1],[5.5 5.8],’k’,’Linewidth’,2) plot([-1.5 -1],[5.8 6.1],’k’,’Linewidth’,2) plot([-1.5 -1],[6.1 6.4],’k’,’Linewidth’,2) axis equal
Comment your code.
A quality report is required for this project. Discuss the problem, formulation, solution, etc (see my Sample Report)
You will be solving and comparing the two problem described in class where you are minimizing the ‘1-norm of the internal forces of the bars. The ‘1-norm problem is solved both weighted and unweighted by the lengths of the bars.
You may only use the linprog()function in Matlab for this project
When describing the formulation of the matrices in your report, it is not going to be possible to show every element of the matrix as I have done in my Sample Report. The following is an example of how to take a possibly very large matrix and describe the necessary pattern for someone to be able to recreate the matrix:
-
We de ne the vector a (of length mN) as
amN T
a =
a1
a2
am
am+1
a2m
(1)
and the matrix A (of size (m + 1)N m) is built from a as
2
A0
3
A =
6
A...
2
7
(2)
6
AN
1
7
6
7
where
2
4
5
3
a1+m k
0
0
6
a1+m k
a2+m k
.
am+m k
7
Ak =
0.
a2+m k
(3)
6
..
. .
7
6
7
6
0
0
am+m
k
7
6
7
4
5
2
