1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
|
//Three carts interconnected by springs, are subjected to the loads P1, P2, and P3. The displacementas of the carts can be found by minimizing the potential energy of the system.
//
//f = 0.5X'[K]X - X'P
//
//where [K] = [k1+k4+k5 -k4 - k5
// -k4 k(2)+k(4)+k(6) -k6
// -k5 -k(6) k3+k5+k6+k7+k8 ]
//The following data is given: k1 = 5000 N/m , k2 = 1500 N/m,
//k3 = 2000 N/m, k4 = 1000 N/m, k5 = 2500 N/m, k6 = 500 N/m, k7 = 3000 N/m, k8 = 3500 N/m
//P1 = 1000 N/m, P2 = 2000 N/m and P3 = 3000 N/m.
//The optimum displacement is x = [0.3241 0.8360 0.3677];
//Reference: Rao, S. S. (2009). Engineering Optimization: Theory and Practice: Fourth Edition. John Wiley and Sons. Chapter 6.DOI: 10.1002/9780470549124.
//======================================================================
// Copyright (C) 2018 - IIT Bombay - FOSSEE
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
// Author:Debasis Maharana
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
//======================================================================
clc
// Given data
k = [5000 1500 2000 1000 2500 500 3000 3500];
p = [1000 2000 3000];
Kval = [k(1)+k(4)+k(5) -k(4) -k(5)
-k(4) k(2)+k(4)+k(6) -k(6)
-k(5) -k(6) k(3)+k(5)+k(6)+k(7)+k(8) ]
//Initial Guess
x0 = [1 1 1];
//Unconstraint,unbounded and continuous problem. Hence the values of intcon,bounds and constraints are giben empty matrices
//Setting Iteration and cpu time in options
options = list("MaxIter", 100, "CpuTime", 100);
//calling the optimization solver
[xopt,fopt,exitflag,output] = intqpipopt(Kval,-p,[],[],[],[],[],[],[],x0,options)
clc
//Result display
select exitflag
case 0
disp("Optimal Solution Found")
printf('\n The displacement of the three springs are \n x1 = %f\n x2 = %f\n x3 = %f',xopt(1),xopt(2),xopt(3));
printf('\nThe potential energy of the system is %f',fopt)
printf('\nThe constraint violation is %f',output.ConstrViolation)
case 1
disp("InFeasible Solution")
printf('\nThe constraint violation is %f',output.ConstrViolation)
case 2
disp("Objective Function is Continuous Unbounded.")
printf('\nThe constraint violation is %f',output.ConstrViolation)
case 3
disp("Limit Exceeded.")
printf('\nThe constraint violation is %f',output.ConstrViolation)
case 4
disp("User Interrupt.")
case 5
disp("MINLP Error.")
end
|
