OPTIMASI BENTUK ROTATING DISK BERDASARKAN TEGANGAN TANGENSIAL DAN VOLUME MENGGUNAKAN OPTIMISASI - Diponegoro University | Institutional Repository (UNDIP-IR)

LAMPIRAN

Contoh langkah untuk mendapatkan Plot Kurva Isomerit pada optimasi Objective
Function 1 dengan variasi variabel L2 dan L3 :

1. Langkah 1, menuliskan pada M-file Matlab seperti berikut:
function [objective3] = ConstructDiskObjectiveFunction3 (x)
L1 =x(1);
L2 =x(1),
L3 =x(2),
L4 =3;
L5 =3;
L6 =3;
%L1, L2, L3, L4, L5, L6 satuannya dalam inches
R2 = 6.0; %inches
R3 = 5;
R4 = 3.5;
R5 = 2;
R6 = 1.0;
N = 100; % rpm
V = 1; % velocity, inch per sec

nu = 0.3; % poisson ratio (v)
rho = 0.284; % density
P2=0.0; % pressure at the outermost ring surface ,psi
P6=1001.0; % internal pressure at the bore, in this case P6=Pm
P1=0; % external pressure at the periphery (P1 = P2)
%An
A2 =
A3 =
A4 =
A

(((3+nu)*rho*10^4)/4)*((R2/R2)^2-(R4/R2)^2);
(((3+nu)*rho*10^4)/4)*((R3/R2)^2-(R5/R2)^2);
(((3+nu)*rho*10^4)/4)*((R4/R2)^2-(R6/R2)^2);
= [A2 A3 A4];

%Bn
B2 =
B3 =
B4 =

B5 =
B

(2*(R2/R3)^2)/((R2/R3)^2-1);
(2*(R3/R4)^2)/((R3/R4)^2-1);
(2*(R4/R5)^2)/((R4/R5)^2-1);
(2*(R5/R6)^2)/((R5/R6)^2-1);
= [B2 B3 B4 B5];

%Cn
C2 =
C3 =
C4 =
C

2/((R3/R4)^2-1);
2/((R4/R5)^2-1);
2/((R5/R6)^2-1);
= [C2 C3 C4];

%Dn
D2 = (((1-nu)+(1+nu)*(R2/R3)^2)/((R2/R3)^2-1))+(L2/L3)*(((1+nu)+(1nu)*(R3/R4)^2)/((R3/R4)^2-1));
D3 = (((1-nu)+(1+nu)*(R3/R4)^2)/((R3/R4)^2-1))+(L3/L4)*(((1+nu)+(1nu)*(R4/R5)^2)/((R4/R5)^2-1));

D4 = (((1-nu)+(1+nu)*(R4/R5)^2)/((R4/R5)^2-1))+(L4/L5)*(((1+nu)+(1nu)*(R5/R6)^2)/((R5/R6)^2-1));
D
= [D2 D3 D4];
%Kn
K2 =
K3 =
K4 =
K

A2/C2;
A3/C3;
A4/C4;
= [K2 K3 K4];

%Un
U2 =

U3 =
U4 =
U

D2/C2;
D3/C3;
D4/C4;
= [U2 U3 U4];

%Qn
Q2 =
Q3 =
Q4 =
Q

(B2/C2)*(L1)/L2;
(B3/C3)*(L2)/L3;
(B4/C4)*(L3)/L4;
= [Q2 Q3 Q4];

P3_g =(200-rand(1,2)*(200-100));%initial guess for P3, 2 random
numbers between 100-200
for n=1:2,
P4_g=(K2*(V^2))-(Q2*P2)+U2*P3_g(1,:);
%calculation for P6
P5_g=(K3*(V^2))-(Q3*P3_g(1,:))+(U3*P4_g);
%using initial guess
of P3
P6_g=(K4*(V^2))-(Q4*P4_g)+(U4*P5_g);
%to obtain linear
equation for interpolation
end
%interpolation, using actual value of P6 to obtain correct value of P3
P3 = (((P6-P6_g(1,1))*(P3_g(1,2)-P3_g(1,1)))/(P6_g(1,2)P6_g(1,1)))+P3_g(1,1);
%calculation of pressure for each interface
P4 = (K2*V^2)-(Q2*P2)+(U2*P3);
P5 = K3*V^2-Q3*P3+U3*P4;
P6 = K4*V^2-Q4*P4+U4*P5;
P = [P2 P3 P4 P5 P6],
%radial stress calculation for each interface

radial_stress3 = -((1+(L2/L3))*P3)/2;
radial_stress4 = -((1+(L3/L4))*P4)/2;
radial_stress5 = -((1+(L4/L5))*P5)/2;
radial_stress6 = -((1+(L5/L6))*P6)/2;
radial_stress = [radial_stress3 radial_stress4 radial_stress5
radial_stress6];
%En
E2 = 1/((R2/R3)^2-1);
E3 = 1/((R3/R4)^2-1);

E4 = 1/((R4/R5)^2-1);
E5 = 1/((R5/R6)^2-1);
E = [E2 E3 E4 E5];
F2 = (((((3+nu)*rho)*10^4)/4)*(R2/R2)^2)+(((1-nu)
*rho*10^4)/4)*(R3/R2)^2;
F3 = (((((3+nu)*rho)*10^4)/4)*(R3/R2)^2)+(((1nu)*rho*10^4)/4)*(R4/R2)^2;
F4 = (((((3+nu)*rho)*10^4)/4)*(R4/R2)^2)+(((1nu)*rho*10^4)/4)*(R5/R2)^2;
F5 = (((((3+nu)*rho)*10^4)/4)*(R5/R2)^2)+(((1nu)*rho*10^4)/4)*(R6/R2)^2;
F = [F2 F3 F4 F5];
%tangential stress (n)

tangential_stress3=-(B2*(L3/L2)*P2)+((E2+(B2/2)nu/2*(L2/L3))*P3)+F2*V^2;
tangential_stress4=-(B3*(L4/L3)*P3)+((E3+(B3/2)nu/2*(L3/L4))*P4)+F3*V^2;
tangential_stress5=-(B4*(L5/L4)*P4)+((E4+(B4/2)nu/2*(L4/L5))*P5)+F4*V^2;
tangential_stress6=-(B5*(L6/L5)*P5)+((E5+(B5/2)nu/2*(L5/L6))*P6)+F5*V^2;
tangential_stress = [abs(tangential_stress3) abs(tangential_stress4)
abs(tangential_stress5) abs(tangential_stress6)],
%nilai tegangan tangensial maksimum
max_sigma_t = max(tangential_stress); %...(1)
%nilai tegangan tangensial minimum
min_sigma_t = min(tangential_stress); %...(2)
%objective3, max sigma(t) - min sigma(t)
%substitusi dari persamaan (1) dan (2)
objective3 = (max_sigma_t - min_sigma_t),
end

Save As M-file di atas dengan nama: ConstructDiskObjectiveFunction3 .

2. Langkah 2, menuliskan constraints kosong pada M-file baru:
function [c, ceq] = constraintL (x)
%Nonlinear inequality constraints

c = [];
%Nonlinear equality constraints
ceq = [];

Save As M-file di atas dengan nama: constraintL.

3. Langkah 3, menuliskan batas atas, batas bawah, fungsi constraint (jika ada) dan
fungsi fmincon pada M-file baru:

clc
clear all
x0 = [0.7 0.7] % Make a starting guess at solution
f = ConstructDiskObjectiveFunction3 (x0)
%x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
options = optimset ('Display', 'iter', 'PlotFcns', @optimplotfval);
[x,fval] = fmincon (@ConstructDiskObjectiveFunction3, x0, [], [], [],
[], [0.6 0.6], [4 4], @constraintL, options)

Jalankan eksekusi optimasi tersebut, dan akan keluar nilai objective function minimum
serta nilai L2 dan L3 yang optimum. Catat senua data pada tiap iterasi, yakni data L2,

L3 dan nilai fungsinya (digunakan pada langkah 6 untuk menunjukkan jalannya
optimisasi dari tebakan awal hingga tercapai optimum).

4. Langkah 4, menuliskan pada M-file baru sebagai berikut:
function [objective3] = ConstructDiskObjectiveFunction3bwt_data (x, y)
L1 =x;
L2 =x;
L3 =y;
L4 =3;
L5 =3;
L6 =3;
R2 = 6.0; %inches
R3 = 5;
R4 = 3.5;
R5 = 2;
R6 = 1.0;
N = 100; % rpm
V = 1; % velocity, inch per sec
nu = 0.3; % poisson ratio (v)
rho = 0.284; % density

P2=0.0; % pressure at the outermost ring surface ,psi
P6=1001.0; % internal pressure at the bore, in this case P6=Pm
P1=0; % external pressure at the periphery (P1 = P2)
%An
A2 =
A3 =
A4 =
A

(((3+nu)*rho*10^4)/4)*((R2/R2)^2-(R4/R2)^2);
(((3+nu)*rho*10^4)/4)*((R3/R2)^2-(R5/R2)^2);
(((3+nu)*rho*10^4)/4)*((R4/R2)^2-(R6/R2)^2);
= [A2 A3 A4];

%Bn
B2 =
B3 =
B4 =
B5 =
B

(2*(R2/R3)^2)/((R2/R3)^2-1);
(2*(R3/R4)^2)/((R3/R4)^2-1);
(2*(R4/R5)^2)/((R4/R5)^2-1);
(2*(R5/R6)^2)/((R5/R6)^2-1);
= [B2 B3 B4 B5];

%Cn
C2 = 2/((R3/R4)^2-1);
C3 = 2/((R4/R5)^2-1);

C4 = 2/((R5/R6)^2-1);
C
= [C2 C3 C4];
%Dn
D2 = (((1-nu)+(1+nu)*(R2/R3)^2)/((R2/R3)^2-1))+(L2/L3)*(((1+nu)+(1nu)*(R3/R4)^2)/((R3/R4)^2-1));
D3 = (((1-nu)+(1+nu)*(R3/R4)^2)/((R3/R4)^2-1))+(L3/L4)*(((1+nu)+(1nu)*(R4/R5)^2)/((R4/R5)^2-1));
D4 = (((1-nu)+(1+nu)*(R4/R5)^2)/((R4/R5)^2-1))+(L4/L5)*(((1+nu)+(1nu)*(R5/R6)^2)/((R5/R6)^2-1));
D
= [D2 D3 D4];
%Kn
K2 =
K3 =
K4 =
K

A2/C2;
A3/C3;
A4/C4;
= [K2 K3 K4];

%Un
U2 =
U3 =
U4 =
U

D2/C2;
D3/C3;
D4/C4;
= [U2 U3 U4];

%Qn
Q2 =
Q3 =
Q4 =
Q

(B2/C2)*(L1)/L2;
(B3/C3)*(L2)/L3;
(B4/C4)*(L3)/L4;
= [Q2 Q3 Q4];

P3_g =(200-rand(1,2)*(200-100));%initial guess for P3, 2 random
numbers between 100-200
for n=1:2,
P4_g=(K2*(V^2))-(Q2*P2)+U2*P3_g(1,:);
%calculation for P6
P5_g=(K3*(V^2))-(Q3*P3_g(1,:))+(U3*P4_g);
%using initial guess
of P3
P6_g=(K4*(V^2))-(Q4*P4_g)+(U4*P5_g);
%to obtain linear
equation for interpolation
end
%interpolation, using actual value of P6 to obtain correct value of P3
P3 = (((P6-P6_g(1,1))*(P3_g(1,2)-P3_g(1,1)))/(P6_g(1,2)P6_g(1,1)))+P3_g(1,1);
%calculation of pressure for each interface
P4 = (K2*V^2)-(Q2*P2)+(U2*P3);
P5 = K3*V^2-Q3*P3+U3*P4;
P6 = K4*V^2-Q4*P4+U4*P5;
P = [P2 P3 P4 P5 P6];
%radial stress calculation for each interface
radial_stress3 = -((1+(L2/L3))*P3)/2;
radial_stress4 = -((1+(L3/L4))*P4)/2;

radial_stress5 = -((1+(L4/L5))*P5)/2;
radial_stress6 = -((1+(L5/L6))*P6)/2;
radial_stress = [radial_stress3 radial_stress4 radial_stress5
radial_stress6];
%En
E2 = 1/((R2/R3)^2-1);
E3 = 1/((R3/R4)^2-1);
E4 = 1/((R4/R5)^2-1);
E5 = 1/((R5/R6)^2-1);
E = [E2 E3 E4 E5];
F2 = (((((3+nu)*rho)*10^4)/4)*(R2/R2)^2)+(((1nu)*rho*10^4)/4)*(R3/R2)^2;
F3 = (((((3+nu)*rho)*10^4)/4)*(R3/R2)^2)+(((1nu)*rho*10^4)/4)*(R4/R2)^2;
F4 = (((((3+nu)*rho)*10^4)/4)*(R4/R2)^2)+(((1nu)*rho*10^4)/4)*(R5/R2)^2;
F5 = (((((3+nu)*rho)*10^4)/4)*(R5/R2)^2)+(((1nu)*rho*10^4)/4)*(R6/R2)^2;
F = [F2 F3 F4 F5];
%tangential stress (n)
tangential_stress3=-(B2*(L3/L2)*P2)+((E2+(B2/2)nu/2*(L2/L3))*P3)+F2*V^2;
tangential_stress4=-(B3*(L4/L3)*P3)+((E3+(B3/2)nu/2*(L3/L4))*P4)+F3*V^2;
tangential_stress5=-(B4*(L5/L4)*P4)+((E4+(B4/2)nu/2*(L4/L5))*P5)+F4*V^2;
tangential_stress6=-(B5*(L6/L5)*P5)+((E5+(B5/2)nu/2*(L5/L6))*P6)+F5*V^2;
tangential_stress = [abs(tangential_stress3) abs(tangential_stress4)
abs(tangential_stress5) abs(tangential_stress6)];
%nilai tegangan tangensial maksimum
max_sigma_t = max(tangential_stress); %...(1)
%nilai tegangan tangensial minimum
min_sigma_t = min(tangential_stress); %...(2)
%objective3, max sigma(t) - min sigma(t)
%substitusi dari persamaan (1) dan (2)
objective3 = (max_sigma_t - min_sigma_t);
end

Save As dengan nama file : ConstructDiskObjectiveFunction3bwt_data.

5. Langkah 5, menuliskan pada M-file baru sebagai berikut:
clc
clear all
x=[0.25:0.25:5];% Make a starting guess at solution
y=[0.25];
for n=1:20
[f(n)] = ConstructDiskObjectiveFunction3bwt_data (x(n),y);
end

Jalankan program di atas, kemudian lihat pada Workspace , klik kiri dua kali pada f.
Terdapat 20 data yang muncul di sana, copy pada excel. Kemudian ulangi langkah 5
dengan mengganti nilai y = 0.25 sampai 5. Lakukan langkah yang sama untuk
mengcopykan data ke excel, sehingga didapat data seperti berikut:
y. x
0,25
0,5
0,75
1
1,25
1,5
1,75
2
2,25
2,5
2,75
3
3,25
3,5
3,75
4
4,25
4,5
4,75
5

0.25
0.5
16539,31
14276,91794
8483,034
7496,999434
5723,873
5108,36504
4335,494
3893,429895
3502,865
3160,752198
2950,029
2672,695149
2557,668
2325,615182
2265,781
2067,096717
2040,906
1921,88339
1928,234
1963,799485
1967,776
2003,669683
2005,715
2041,734689
2042,18
2078,178721
2077,28
2113,1482
2111,106
2146,763143
2143,738
2179,124408
2175,248
2210,318488
2205,7
2240,420782
2235,15
2269,497909
2263,652
2297,609377

0,75
12235,46
6569,94
4521,074
3468,37
2830,216
2403,855
2100,115
1910,636
1955,968
1998,525
2038,754
2076,976
2113,428
2148,297
2181,728
2213,845
2244,748
2274,525
2303,251
2330,993

1
10384,07
5696,719
3960,103
3059,351
2510,679
2143,124
1892,408
1942,82
1989,216
2032,44
2073,057
2111,464
2147,953
2182,747
2216,021
2247,917
2278,553
2308,027
2336,424
2363,818

1,25
8697,403
4872,778
3423,721
2665,482
2201,601
1890,14
1922,111
1974,177
2021,657
2065,573
2106,604
2145,222
2181,774
2216,519
2249,66
2281,361
2311,752
2340,945
2369,033
2396,097

1,5
7154,39929
4124,489732
3036,563916
2426,966645
2025,104136
1890,222622
1951,010596
2004,738025
2053,320353
2097,950897
2139,419218
2178,274046
2214,912708
2249,633088
2282,665276
2314,191624
2344,359913
2373,292248
2401,091238
2427,844381

1,75
7434,678
4484,717
3272,567
2592,659
2146,11
1915,858
1979,137
2034,534
2084,234
2129,599
2171,527
2210,641
2247,39
2282,108
2315,053
2346,427
2376,393
2405,084
2432,613
2459,073

2
8010,465
4826,201
3498,864
2752,537
2263,34
1940,764
2006,522
2063,592
2114,424
2160,541
2202,95
2242,345
2279,225
2313,963
2346,842
2378,083
2407,866
2436,335
2463,611
2489,796

2,25
8542,764
5150,368
3716,041
2906,902
2376,969
1996,36
2033,194
2091,941
2143,915
2190,801
2233,709
2273,405
2310,438
2345,215
2378,047
2409,175
2438,793
2467,058
2494,099
2520,025

Gambar A Data objective function 1.

Gambar A tersebut hanya sebagian data saja (karena datanya terlalu panjang, sebagian
data tidak penulis munculkan).

6. Langkah 6, menuliskan pada M-file baru sebagai berikut:
clc
clear all
x = [0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5;
0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5;
0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5;
0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5; 0.25:0.25:5];
y = x';
z =[16539.31255 14276.91794 12235.45734 10384.07445 8697.403333
7154.39929 7434.678239 8010.465258 8542.764282 9036.32286
9495.221759 9922.988051 11134.42487 12357.54697 12539.61864
12226.61846 11931.7736 11983.21473 12260.69824 12523.37484
8483.034169 7496.999434 6569.940144 5696.718889 4872.778123
4124.489732 4484.716703 4826.200802 5150.367747 5458.502229

5
3
3
2
2
2
2
2
2
2
2
2

2
2
2
2
2

5751.764935
8280.426845
5723.87297
3036.563916
4125.154418
6247.655319
4335.494207
2426.966645
3200.194015
4721.611788
3502.864886
2025.104136
2594.066327
3716.550397
2950.02924
1890.222622
2160.091502
3249.748449
2557.667845
1951.010596
2084.508174
2543.882655
2265.780862
2004.738025
2146.608762
2517.317767
2040.905898
2053.320353
2200.896893
2499.465612
1928.23444
2097.950897
2249.363157
2623.052634
1967.776042
2139.419218
2293.319778
2606.028006
2005.714934
2178.274046
2333.671188
2476.382476
2042.180359
2214.912708
2371.064302
2512.913211
2077.27997
2249.633088
2405.976613
2548.442198
2111.105807
2282.665276
2438.770228
2581.418931
2143.738157
2314.191624

6031.207148
8133.462958
5108.36504
3272.567275
4318.050506
6371.467325
3893.429895
2592.659171
3339.627262
5103.321444
3160.752198
2146.109627
2697.833534
4021.864417
2672.695149
1915.858034
2238.652109
3494.211658
2325.615182
1979.137353
2109.200918
2722.572769
2067.096717
2034.533802
2172.976146
2678.379178
1921.88339
2084.233849
2228.432166
2646.391642
1963.799485
2129.598654
2277.706911
2755.658549
2003.669683
2171.526908
2322.210392
2729.21162
2041.734689
2210.641108
2362.914267
2593.725134
2078.178721
2247.390039
2400.513025
2585.021979
2113.1482
2282.108425
2435.518658
2579.106707
2146.763143
2315.053305
2468.318803
2608.485724
2179.124408
2346.427111

6650.846687
7992.567091
4521.073931
3498.863958
4650.935495
6275.600288
3468.369626
2752.537434
3502.597816
5274.209214
2830.216218
2263.339808
2798.597505
4318.938245
2403.85469
1940.764172
2315.126224
3732.661307
2100.115062
2006.522257
2133.282669
2897.098984
1910.635898
2063.592384
2198.729161
2835.894369
1955.968131
2114.423704
2255.358512
2790.238713
1998.524939
2160.540932
2305.45219
2885.631303
2038.754367
2202.949566
2350.515825
2850.043068
2076.976037
2242.344554
2391.587012
2708.885636
2113.428492
2279.225377
2429.407034
2693.259526
2148.296591
2313.963152
2464.521891
2681.302564
2181.728166
2346.841607
2497.344438
2672.250072
2213.844591
2378.083104

7426.35978
7857.371031
3960.102799
3716.040744
5202.661761
6182.948808
3059.35082
2906.902198
3921.836408
5201.36296
2510.679107
2376.968649
3079.791269
4553.399048
2143.123558
1996.359669
2477.913158
3965.316594
1892.40758
2033.194274
2173.400103
3072.503077
1942.819754
2091.940796
2223.889032
2989.979187
1989.215808
2143.915033
2281.695909
2931.102602
2032.440187
2190.801061
2332.617752
3013.048556
2073.057138
2233.708883
2378.253677
2968.589085
2111.463941
2273.404584
2419.705948
2821.92429
2147.952784
2310.43757
2457.761858
2799.567299
2182.746596
2345.21489
2493.000918
2781.731184
2216.020844
2378.046688
2525.860893
2767.493575
2247.917336
2409.175092

8167.73849
7867.848963
3423.721092
3924.638048
5734.551399
6093.353769
2665.482205
3056.033832
4327.972812
5130.628338
2201.600854
2487.159589
3402.648517
4493.294387
1890.140289
2079.357831
2741.847865 2999.04129
1922.111425
2059.180885
2360.877829
3268.235712
1974.17664
2119.604758
2352.589017
3140.744483
2021.656882
2172.731802
2349.360697
3069.075159
2065.573256
2220.401353
2359.221577 2487.73272
2106.603847
2263.825645
2405.44085 2480.42287
2145.222309
2303.840589
2447.286967
2932.899204
2181.773764
2341.044737
2485.592448
2903.996452
2216.518826
2375.8806
2520.969826
2880.438016
2249.660387
2408.68445
2553.881449
2861.149809
2281.360586
2439.718013

2469.726285
2639.295216
2175.24814
2344.359913
2499.067618
2641.136378
2205.699517
2373.292248
2526.974095
2668.408032
2235.149999
2401.091238
2553.593282
2694.225207
2263.652209
2427.844381
2607.864659
2745.419138

2499.213825
2665.925168
2210.318488
2376.392813
2528.441249
2668.168648
2240.420782
2405.084161
2556.192319
2695.352899
2269.497909
2432.612789
2582.623503
2721.048194
2297.609377
2459.073259
2636.232505
2771.692783

2528.19407
2756.15546
2244.747729
2407.865724
2557.322882
2694.766335
2274.524647
2436.334825
2584.933417
2721.875021
2303.250924
2463.611056
2611.191001
2747.460023
2330.993006
2489.79605
2664.161944
2797.575489

2556.68 2584.684155 2612.218655
2845.316577
2278.553283 2311.751945
2438.793204 2469.189309
2585.724776 2613.658786
2747.178131 2832.30902
2308.027437 2340.944902
2467.057944 2497.266765
2613.208982 2641.030233
2747.984271 2821.634187
2336.424367 2369.033037
2494.09896 2524.089003
2639.306752 2666.981388
2773.470077 2812.900898
2363.817506 2396.096807
2520.024956 2549.771793 2579.048
2691.663059 2718.74563
2823.075916];

%batas bawah
hold on;
m = [0.25; 5];
n = [0.6; 0.6];
plot (m, n,'-k');
hold on;
o = [0.6; 0.6];
p = [0.25; 5];
plot (o, p,'-k');
%batas atas
hold on;
q = [4; 4];
r = [0.25; 5];
plot (q, r,'-k');
hold on;
s = [5; 0.25];
t = [4; 4];
plot (s, t,'-k');
%iterasi optimasi
hold on;
a = [0.7000;4.0000;3.5101;2.0550;1.3275;1.4775;1.4775;1.4922;1.4931;
1.4914;1.4357;1.4340;1.4275;1.4273;1.4272;1.4272;1.4272;1.4276;1.4282;
1.4282;1.4353];
b = [0.7000;4.0000;4.0000;2.3000;1.4500;1.3969;1.3969;1.3844;1.3829
;1.3814;1.3688;1.3697;1.3682;1.3681;1.3681;1.3681;1.3681;1.3678;1.3673
;1.3672;1.3612];
plot (a, b,':k');
hold on;
c = [0.7000;1.4353];

d = [0.7000;1.3612];
plot (c, d,'+k');
hold on;
e = [2.0000;1.6500;1.3875;1.4315;1.4321;1.4268;1.4207;1.4272;1.4277
;1.4295;1.4297;1.4297;1.4297;1.4297;1.4297;1.4297;1.4297;1.4297];
f = [2.0000;1.6500;1.3875;1.3629;1.3835;1.3782;1.3721;1.3761;1.3744
;1.3684;1.3676;1.3675;1.3675;1.3675;1.3675;1.3675;1.3675;1.3675];
plot (e, f,':r');
hold on;
g = [2.0000;1.4297];
h = [2.0000;1.3675];
plot (g, h,'+r');
hold on;
i = [1.0000;0.8000;0.7875;0.7846;0.7838;0.7838;0.7838;0.7838;0.7838;
1.154 ;1.3694;1.4234;1.4266;1.4274;1.4278;1.4279;1.4279;1.4280];
j = [3.5000;2.0500;1.9594;1.9381;1.9329;1.9326;1.9324;1.9324;1.9324;
1.5993;1.4064;1.3579;1.3550;1.3543;1.3539;1.3538;1.3538;1.3537];
plot (i, j,':g');
hold on;
k = [1.0000;1.4280];
l = [3.5000;1.3537];
plot (k, l,'+g');

Save As program di atas dan jalankan.

7. Langkah 7, menuliskan pada Command Window: >> contour (x,y,z)
Kemudian untuk menampakkan garis proses jalannya optimasi dari tebakan awal
hingga tercapai optimum, Run kembali M-file pada langkah 6.

Gambar B Hasil plot kurva isomerit.