Truss Topology Project

Truss Topology Project

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.
0 5 10 15 20
0
2
4
6
8
10
Figure 1: This figure shows the three anchors along with the grid of possible link connects
(which are fixed) 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 define the vector a (of length mN) as
a =

a1 a2 · · · am am+1 · · · a2m · · · amN T
(1)
and the matrix A (of size (m + 1)N × m) is built from a as
A =





A0
A2
.
.
.
AN−1





(2)
where
Ak =







a1+m∗k a2+m∗k · · · am+m∗k
−a1+m∗k 0 · · · 0
0 −a2+m∗k
.
.
.
.
.
.
0 · · · 0 −am+m∗k







(3)
2