CHAPTER
7
Optimum Design with MATLAB®
7.1 ________________________________________________________________________________
Formulate and solve Exercise 3.34
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7.9 _______________________________________________________________________________
7.10 ______________________________________________________________________________
Formulation: Units of N and cm are used
1. Design variables: x1 = b, x2 = t1, x3 = t2, x4 = h
2. Cost function: f = L (2x1x2+x3x4) = 150(2x1x2+x3x4)
3. Constraints:
<axial stress> g1 = (Mc/I + Pcos
θ
/A)/
σ
a − 1.0 ≤ 0,
where M = PLsin
θ
, c = x2 + x4/2, I = [x1(2x2+ x4)3 − (x1− x3) x
3
4
]/12, A = 2x1x2 + x3x4,
7.11 ______________________________________________________________________________
Formulation:
1ii
i
=
1i
i
=
3. Constraints (18 stress constraints)
gj =
σ
1 j/5000 − 1.0 ≤ 0, j = 1,2,3; g3 + j = −
σ
1 j/5000 −1.0 ≤ 0, j = 1,2,3;
7.12 ______________________________________________________________________________
Formulation: Minimize f = (x2 − x3)2;
subject to h1 =
φ
2x1(x1− x2 + x3)/x2x3 − 1 = 0, h2 = 1.0 − x2(1 − x1+ x2)/
φ
3x1 = 0,