EN3098 – Engineering Optimization with Python Coursework 23/24
Engineering Optimization Coursework
1. Design of a Three-Bar Truss
The optimal design of the three-bar truss shown in Fig. 5- 1 is considered using two different objectives with the cross-sectional areas of members 1 (and 3) and 2 as design variables.
Figure 5- 1 Three-bar truss.
By considering the weight and the vertical deflection of the loaded joint as objectives for minimization, the optimization problem can be stated as follows:
Find
which minimizes
or/and
subject to
where
Let P = 20 , H = 1 and E = 1 , σ(u) = 20 , σ(l) = −15 , A(u) = 5.0, A(l) = −0. 1 (i = 1, 2), determine the optimization solutions X∗ for the following three cases:
(a) Minimize f1 .
(b) Minimize f2
(c) Minimize both f1 and f2 , simultaneously, with equal weighting.
Hint: the negative value of a stress indicates a compression, only. The 3rd constrain σ3 ≤ σ(l) implies that the compression stress should not exceed the threshold limit.
Coursework
(1) Develop an optimization programme with Python for this optimization problem, including
. Print the solution in each iterative step.
. Plot the optimization process and check the convergence graphically.
. Print the final optimal solution.
(2) Write a Coursework Report (comply with EN3098 Report Writing Guidelines).
Submission
Please submit both of your Python programme and Coursework Report to the link provided in Learning Central before 7th May 2024.