Cantilever Beam, end load:
δ
= [FL
3
]/[3EI] [constraint]
Rectangular section, A = bt; I = bt
3
/12; m = bLt
ρ
[objective function]
, δ
= [4FL
3
/[Ebt
3
]
[a] b and L fixed, t free
°
t
3
= [4FL
3
]/[Eb
δ
]
°
t
3
= m
3
/[b
3
L
3
ρ
3
]
°
m
3
= [4Fb
2
L
6
ρ
3
]/[E
δ
]
°
m = [4F/
δ
]
1/2
[b
1/2
L]
2
[
ρ
/E
1/3
]
°
M
1
= E
1/3
/
ρ
°
log[M
1
] = [1/3]log[E] - log[
ρ
]; log[E] = 3log[M
1
] + 3log[
ρ
]
°
M
1
has a numerical value of [100*10
9
N*m
-2
]
1/3
/1.0 Mg*m
-3
=
°
M
1
= 4640 N
1/3
*m
7/3
/Mg
Example
°
F = 100N, b = 0.3m, d = 0.05m, L = 2m
°
m = 7.73x10
-3
Mg = 7.73 kg
°
for flexible low density foam [
r
= ~ 0.02 Mg/m
3
], t = 64 cm!

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