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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.