Q2 Strength and stiffness constraints in a cantilever beam Design problem: A square

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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