Engineering Optimization: Theory and Practice, Fourth Edition

62 Introduction to Optimization

x 2

x 1

p 0 per unit length

Cross-section

P

L

L

2

Figure 1.33 A simply supported beam subjected to concentrated and distributed loads.

(a)Formulate the problem as a mathematical programming problem assuming that

the cross-sectional dimensions of the beam are restricted asx 1 ≤x 2 , 0. 04 m≤x 1

≤ 0. 12 m, and 0. 06 m≤x 2 ≤ 0. 20 m.

(b)Find the solution of the problem formulated in part (a) using MATLAB.

(c)Find the solution of the problem formulated in part (a) graphically.

1.33 Solve Problem 1.32, parts (a), (b), and (c), assuming the cross section of the beam to

be hollow circular with inner diameterx 1 and outer diameterx 2. Assume the data and

bounds on the design variables to be as given in Problem 1.32.

1.34 Find the solution of Problem 1.31 using MATLAB.

1.35 Find the solution of Problem 1.2(a) using MATLAB.

1.36 Find the solution of Problem 1.2(b) using MATLAB.