Homework answers / question archive / EG2501 Design & MATLAB Assignment Module Code & Title: EG2501 Design & Computing in Engineering 1 Learning Outcomes • Understanding of fundamentals of engineering design optimisation and formulating an engineering design problem in the form of an optimisation problem • Coding an engineering design optimisation problem in MATLAB • Development of GUIs in MATLAB • Structuring and wiring a programme with multiple files • Making and using mat-files 2 Background Pressure vessels have applications in many engineering sectors

EG2501 Design & MATLAB Assignment Module Code & Title: EG2501 Design & Computing in Engineering 1 Learning Outcomes • Understanding of fundamentals of engineering design optimisation and formulating an engineering design problem in the form of an optimisation problem • Coding an engineering design optimisation problem in MATLAB • Development of GUIs in MATLAB • Structuring and wiring a programme with multiple files • Making and using mat-files 2 Background Pressure vessels have applications in many engineering sectors

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EG2501 Design & MATLAB Assignment

Module Code & Title: EG2501 Design & Computing in Engineering

1 Learning Outcomes

• Understanding of fundamentals of engineering design optimisation and formulating an engineering design problem in the form of an optimisation problem

• Coding an engineering design optimisation problem in MATLAB

• Development of GUIs in MATLAB

• Structuring and wiring a programme with multiple files

• Making and using mat-files

2 Background

Pressure vessels have applications in many engineering sectors. These structures are normally made of high strength alloys and are subjected to an internal pressure higher than the ambient pressure.

Pressure vessel design summary

In design of pressure vessels to operate at an internal pressure of ? (in Pa) with a capacity of ? (in m3) the designer needs to find the dimensions and material of the vessel such that the von Mises stress (?′) is less than the allowable stress (????) and the internal volume (??) is equal to the desired capacity ?. Normally, there are constraints on the overall size of the vessel ?? and ? (in

?), as well as the dry mass of the vessel ?? (in ??).

Figure 1-Cylindrical pressure vessel with semi-spherical caps and definition of size parameters

A

A

Section A-A

L

t

ro=ri+t

r

i

r

o

LT

H

EG2501 Design & MATLAB Assignment

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Design model summary

Allowable stress (based on a desired factor of safety of ??):

???? =

??

??

(1)

Vessel internal volume (capacity):

?? = ???

2

? + 4???

3

/3 (2)

von Mises stress:

?′ = √

(??−??

)2+(??−??

)2+(??−??

)2

2

(3)

The stress components which are used to calculate the von Mises stress are different in

thin-walled and thick-walled pressure vessels as shown below:

Case thin-walled: ?⁄?? < 0.05

?? =

???

?

(4.a)

?? = 0 (4.b)

?? =

???

2?

(4.c)

Case thick-walled: ?⁄?? ≥ 0.05

?? =

??

2?

??

2−??

2

(1 +

??

2

??

2

) (5.a)

?? =

??

2?

??

2−??

2

(1 −

??

2

??

2

) (5.b)

?? =

??

2?

??

2−??

2

(5.c)

Vessel material volume:

???? = 2???

?? + 4???

2

? (6)

Vessel dry mass (assuming ?????? = 7850 ??/?3

):

?? = ???? × 7850 (7)

Vessel cost index:

?? = ???? × ??; CF from Table 1 (8)

Overall size:

?? = ? + 2?? (9)

? = 2?? (10)

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Table 1 shows a number of common materials used for cylindrical pressure vessels. These materials have different manufacturing cost. The last column in the table (cost factor) is a parameter identifying how expensive (per unit volume) is a material compared to the first material

in the table.

Table 1-Materials

Material

Number Sy (MPa) Available Thicknesses (mm)

Cost factor

CF

1 170 2,4,6,8,10,20,30 1

2 280 2,3,4,6,8,10,12,14,16,18,20 1.37

3 180 2,4,6,10,20 1.1

4 300 2,4,6,10,20 1.47

5 190 2,4,6,10,20 1.13

6 320 2,4,6,10,20 1.57

7 220 2,4,6,10,20 1.08

8 370 2,3,4,6,7,8,9,10,12,14,16 1.81

9 210 2,4,6,8,10,14,16,20,30,40 1.03

10 390 2,3,4,6,8,10,12,14,16,18,20 1.91

11 260 2,4,6,8,10,12,16,20,30,40,50 1.27

12 440 2,4,6,8,10 2.16

13 270 2,3,4,5,6,7,8,9,10 1.32

14 460 1,2,3,4,5,6,7,8,9,10 2.25

15 290 2,4,6,8,10,12,18,20,30 1.42

16 490 2,3,4,5,6,7,8,9,10 2.4

17 310 2,3,4,5,6,7,8,9,10 1.52

18 530 10,20,30 2.6

19 340 4,5,8,14,20 1.67

20 580 2,4,6,8,10 2.84

21 370 2,4,6,8,10,15,18,20 1.81

22 420 2,4,6,8,10,12,14 2.06

23 460 1,2,4,6,8,10,12 2.25

Note: The data in this table are saved in a mat-file called MaterialFile.mat, in the form of the

following cell structure:

mat.number

mat.sy

mat.t

mat.cf

The file is available from MyAberdeen-Assignment 1 folder

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3 Tasks

Task 1 [30%]

Formulate the design problem above in the form of a standard optimisation problem. Include

constraints on the overall size of the vessel (LT and H must be less than or equal to LT,c and Hc

respectively):

• Identify design variables

• Identify design qualities

• Select optimisation objective

• State all constraints

• Explain how you deal with equality constraints (if there is any)

Note: Marks will be deducted for missing/wrongly identified/not justified design variables, design

qualities, objective, constraints and not reporting the optimisation problem in standard format.

Task 2 [70%]

Write an optimisation programme with a graphical user interface that gets the following inputs:

• internal pressure ? (in bars), capacity ? (in litres), a desired factor of safety ?? and the

constrained values for ??,? and ??

 ( in metres)

• search parameter(s)

and then finds and shows:

• the optimal size (??

, L and t), the index of the optimum material (from Table 1 above), and

the type of the optimal solution (thin-walled or thick-walled), as well as

• allowable stress, von Mises stress, volume of the material, cost index, the overall

dimensions ?? and ?, and the dry mass

OR

• a suitable message in case no feasible solutions is found.

Note: Marks will be deducted if the programme does not find or show the right results, if GUI does

not show all requested parameters, if outputs are not rounded to a reasonable engineering

precision, if there is missing parameter name or unit on the GUI or unit in the optimiser, if there is

missing definition/ necessary comment in the optimiser, for unclear programme structure, and for

uncaptured output error.

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4 Report

A word-processed report including the following essential parts:

• Signed Plagiarism Cover Sheet

• Table of contents

• Maximum 2 pages on the optimisation problem formulations and the optimisation method

(Task 1).

• Two legible screenshots of the GUI of the programme for two optimisation problems with

the following inputs:

o Problem 1: ? = 80 ??? /(???? ??????); ?? = 140 ?????? × (???? ??????) ;

?? = 2; ? ≤ 3 ?; ?? ≤ 10 ?; ?? ≤ 450??

o Problem 2: ? = 8 ??? × (???? ??????); ?? = 800 ?????? /(???? ??????) ;

?? = 3; ? ≤ 2 ?; ?? ≤ 7 ? ; ?? ≤ 160??

???? ?????? = ??? ???? ????? ?????? ?? ???? ??????? ??/??

For both problems, use an increment (grid size) of 5 mm for ??

.

• Programme listing; copy the m-files from the MATLAB editor (keep the MATLAB original

formatting and the text colours but use a font size of 10) and paste them in this section of

your report as text (not image).