section cantilever beam of length L must meet, simultaneously, targets for strength (ability to
support an end load F without failing by plastic yielding) and stiffness S (end deflection must
be less than 5) and it must do this at a minimum weight. The requirements are
Function: cantilever beam
Constraints: must not fail by yielding under end load F; end deflection must be less than 8;
minimum fracture toughness is 7 MPa m¹/2; length L and load F are specified
Objective: minimize mass, m
Free variables: section area A and choice of materials
Hypothetical values to fix the coupling lines (one & imposes a rather fiercer stiffness constraint,
the other is more relax)
Parameter
Value
10 KN
1.5m
0.002m
0.1m
F
L
$₁
$2
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Fig: 1