Pressure Vessels Design Assignment Help Online

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 𝑃(in Pa) with a capacity of 𝐶(in

m3) the designer needs to find the dimensions and material of the vessel such that the von Mises

stress (𝜎′) is less than the allowable stress (𝜎) and the internal volume (𝑉) is equal to the desired capacity 𝐶. Normally, there are constraints on the overall size of the vessel 𝐿𝑇and 𝐻.

Formulate the design problem above in the form of a standard optimization problem. Include constraints on the overall size of the vessel (LT and H):

• Identify design variables

• Identify design qualities

• Select optimization objective

• State 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 optimization problem in standard format.

Write an optimization program with a graphical user interface that gets the following inputs:

• internal pressure 𝑃(in bars), capacity 𝐶(in liters), a desired factor of safety 𝑛𝑑and the

constrained values for 𝐿𝑇and 𝐻( in meters)

• search parameter(s)

and then finds and shows:

• the optimal size (𝑟, L and t), 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

dimensions𝐿𝑇and 𝐻.

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, and for missing parameter name or unit on the GUI, for missing unit in the optimiser, for missing definition/ necessary comment in the optimiser, for unclear programme structure, and for uncaptured output error.

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).

𝑖

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

o Problem 1: 𝑃 = 400 𝑏𝑎𝑟 /(93.7); 𝑉 = 1400 𝑙𝑖𝑡𝑟𝑒𝑠 × (93.7) ;

𝑖

o Problem 2: 𝑃 = 45 𝑏𝑎𝑟 × (93.7); 𝑉 = 700 𝑙𝑖𝑡𝑟𝑒𝑠/(93.7) ;

𝑛𝑑=2; 𝐻≤3.5𝑚; 𝐿𝑇≤7𝑚

𝑛𝑑=2; 𝐻≤3.5𝑚; 𝐿𝑇≤11𝑚

𝒚𝒐𝒖𝒓𝒏𝒖𝒎𝒃𝒆𝒓 = 93.7

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

• 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).

 MATLAB Script Output

You should just run script “main1” in MATLAB

Another example

After run

function main1()

% A GUI for Pressure Vessel Design

% Create a figure and axes

f = figure('Resize','off', 'NumberTitle','off', 'Name','Pressure Vessel Design',...

    'ToolBar','none', 'MenuBar','none', 'Units','pixels', 'Visible','off');

axes('Units','pixels', 'Visible','off');

aPos = get(gca, 'Position'); set(gca, 'Position',[0 aPos(2:4)])

gPos = get(gcf, 'Position'); set(gcf, 'Position',[1 1 1.3 1.3].*gPos)

movegui(gcf, 'center')

gPos = get(gcf, 'Position');

aPos = get(gca, 'Position');

aPos(2) = 15 + (gPos(4) - aPos(4))/2; set(gca, 'Position', aPos)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

a = get(gca, 'Position'); g = get(gcf, 'Position');

ytxt = a(2)+a(4)+ (100:-35:-320) -50;

% yedt = ytxt - 20;

%% Inputs

% Create static text box for labeling

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(1)-15 150 45],...

    'String','Inputs', 'FontSize',20, 'FontWeight','bold');

% internal pressure, P

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(2) 150 20],...

    'String','Internal Pressure, P :', 'FontSize',12);

h.edit1 = uicontrol('Parent',f,'Style', 'edit',...

    'String','10', 'FontSize',12,...

    'Position', [195 ytxt(2) 100 20],...

    'Callback', @P_Callback);

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[300 ytxt(2) 100 20],...

    'String','bars', 'FontSize',12);

% capacity [litres]

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(3) 150 20],...

    'String','Capacity, C :', 'FontSize',12);

h.edit2 = uicontrol('Parent',f,'Style', 'edit',...

    'String','20000', 'FontSize',12,...

    'Position', [195 ytxt(3) 100 20],...

    'Callback', @C_Callback);

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[300 ytxt(3) 100 20],...

    'String','litres', 'FontSize',12);

% desired Factor of Safety

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(4) 150 20],...

    'String','Factor of Safety, nd :', 'FontSize',12);

h.edit3 = uicontrol('Parent',f,'Style', 'edit',...

    'String','2', 'FontSize',12,...

    'Position', [195 ytxt(4) 100 20],...

    'Callback', @nd_Callback);

% constraint on LT [m]

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(5) 150 20],...

    'String','Max of LT :', 'FontSize',12);

h.edit4 = uicontrol('Parent',f,'Style', 'edit',...

    'String','20', 'FontSize',12,...

    'Position', [195 ytxt(5) 100 20],...

    'Callback', @LTMax_Callback);

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[300 ytxt(5) 100 20],...

    'String','m', 'FontSize',12);

% constraint on H [m]

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[50 ytxt(6) 150 20],...

    'String','Max of H :', 'FontSize',12);

h.edit5 = uicontrol('Parent',f,'Style', 'edit',...

    'String','8', 'FontSize',12,...

    'Position', [195 ytxt(6) 100 20],...

    'Callback', @HMax_Callback);

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[300 ytxt(6) 100 20],...

    'String','m', 'FontSize',12);

%% Create push button for ruuning

push_run = uicontrol('Style', 'pushbutton', 'String','Run',...

    'Position',[a(3)-320 a(2)+80 80 45], 'FontSize',20, 'FontWeight','bold',...

    'Callback', @push_run_Callback);

%% Ouputs

% Create static text box for labeling

uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(1)-15 380 45],...

    'String','Outputs', 'FontSize',20, 'FontWeight','bold');

% optimal ri

ri = [];

h.txt1 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(2) 380 20],...

    'String',mynum2str('Optimal ri',ri,'m'), 'FontSize',12);

% optimal L

L = [];

h.txt2 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(3) 380 20],...

    'String',mynum2str('Optimal L',L,'m'), 'FontSize',12);

% optimal t

t = [];

h.txt3 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(4) 380 20],...

    'String',mynum2str('Optimal t',t,'mm'), 'FontSize',12);

% the optimum material (from Table 1)

im = [];

h.txt4 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(5) 380 20],...

    'String',mynum2str('Optimmum material',im,[]'), 'FontSize',12);

% the type of the optimal solution (thin-walled or thick-walled)

walType = [];

h.txt5 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(6) 380 20],...

    'String',mynum2str('Type',walType,[]), 'FontSize',12);

% allowable stress

Sall = [];

h.txt6 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(7) 380 20],...

    'String',mynum2str('Allowable stress',Sall,'MPa'), 'FontSize',12);

% von Mises stress

Svm = [];

h.txt7 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(8) 380 20],...

    'String',mynum2str('von Mises stress',Svm,'MPa'), 'FontSize',12);

% volume of the material

Vmat = [];

h.txt8 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(9) 380 20],...

    'String',mynum2str('volume of the material',Vmat,'m^3'), 'FontSize',12);

% cost index

CI = [];

h.txt9 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(10) 380 20],...

    'String',mynum2str('Cost index',CI,[]), 'FontSize',12);

% the overall dimension LT

LT = [];

h.txt10 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(11) 380 20],...

    'String',mynum2str('LT',LT,'m'), 'FontSize',12);

% the overall dimension H

H = [];

h.txt11 = uicontrol('Style','text','HorizontalAlignment','left',...

    'Position',[a(3) ytxt(12) 380 20],...

    'String',mynum2str('H',H,'m'), 'FontSize',12);

% Make figure visble after adding all components

set(f,'Visible','on')

%% Callback functions -----------------------------------------------------

functionP_Callback(source,callbackdata) %#ok

end

functionC_Callback(source,callbackdata) %#ok

end

functionnd_Callback(source,callbackdata) %#ok

end

functionLTMax_Callback(source,callbackdata) %#ok

end

functionHMax_Callback(source,callbackdata) %#ok

end

functionpush_run_Callback(source,callbackdata) %#ok

        % read the input data from GUI

        P = str2double(get(h.edit1,'String'));

        C = str2double(get(h.edit2,'String'));

nd = str2double(get(h.edit3,'String'));

LTMax = str2double(get(h.edit4,'String'));

HMax = str2double(get(h.edit5,'String'));

        % read data of Table 1

        mat.im = (1 : 23)';

mat.Sy = xlsread('table1.xlsx','Sheet1','B2:B24');% [MPa]

        mat.CF = xlsread('table1.xlsx','Sheet1','D2:D24');

        [~,mat.t] = xlsread('table1.xlsx','Sheet1','C2:C24');% [mm]

        % unit conversion

        P = P*1e5; % bar to Pa

        C = C*1e-3; % liter to m^3

mat.Sy = mat.Sy*1e6;% MPa to Pa

        % optimization

        LB = [1 1 0 ];% lower bounds

        UB = [23 12 HMax];% upper bounds

opts = gaoptimset(@ga);

opts = gaoptimset(opts, 'PopulationSize',100,...

            'Generations',1000,...

            'TolFun',1e-10,...

            'TolCon',1e-5);

        [x,f] = ga(@(x) objF(x,P,C,nd,mat), 3, [],[],[],[],LB,UB,...

            @(x) nLinConstr(x,P,C,nd,LTMax,mat),1:2,opts);

        c = nLinConstr(x,P,C,nd,LTMax,mat);

if any(c > 0)

fprintf('The question has no solution; change the inputs.\n')

return

else

im = x(1);

it = x(2);

            H = x(3);% [m]

ro = H/2;% [m]

            t = mat.t{im}; t = textscan(t,'%n %*c'); t = t{1}; t = t(it)*1e-3;% [m]

ri = ro - t;% [m]

            L = (C - 4*pi*ri^3/3)/(pi*ri^2);% [m]

if t/ri< 0.05

walType = 'thin-walled';

else % t/ri>= 0.05

walType = 'thick-walled';

end

Sy = mat.Sy(im);% [Pa]

Sall = Sy/nd;% allowable stress [Pa]

            [St,Sr,Sl] = pvstress(P,ri,t);% [Pa]

Svm = sqrt(((St - Sr)^2 + (St - Sl)^2 + (Sl - Sr)^2)/2);% von Mises stress [Pa]

Vmat = 2*pi*ri*t*L + 4*pi*ri^2*t;

            CF = mat.CF(im);

            CI = Vmat*CF;

            LT = L + 2*ro;% [m]

end

        % update the outputs

set(h.txt1, 'String',mynum2str('Optimal ri',ri,'m','%.3f'));

set(h.txt2, 'String',mynum2str('Optimal L',L,'m','%.3f'));

set(h.txt3, 'String',mynum2str('Optimal t',t*1e3,'mm'));

set(h.txt4, 'String',mynum2str('Optimmum material',im,[]'));

set(h.txt5, 'String',mynum2str('Type',walType,[]));

set(h.txt6, 'String',mynum2str('Allowable stress',Sall*1e-6,'MPa'));

set(h.txt7, 'String',mynum2str('von Mises stress',Svm*1e-6,'MPa'));

set(h.txt8, 'String',mynum2str('volume of the material',Vmat,'m^3','%.3f'));

set(h.txt9, 'String',mynum2str('Cost index',CI,[]));

set(h.txt10, 'String',mynum2str('LT',LT,'m','%.3f'))

set(h.txt11, 'String',mynum2str('H',H,'m','%.3f'))

end

end