Composite Materials Research Progress

Optimization of Laminated Composite Structures… 53
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* global
X
a
(k)
S
no
X
( k+
1)
b
(k)
X
α
Initial design
Structural analysis
Optimization
New design
Optimal design ?
yes
End
* local
X
g j (X)
Figure 2.1. Illustration of an optimization problem and its solution.
In structural optimization, the design functions can be global as the weight, the stiffness,
the vibration frequencies, the buckling loads, or local as strength constraints, strains and
failure criteria. When the design variables are linked to the transverse properties of the
structural members (e.g. the cross-section area of a bar in a truss), the related optimization
problem is called optimal sizing (Figure 2.2a). The value of some geometric items (e.g. a
radius of an ellipse) can also be variable: in this case, we are talking about shape optimization
(Figure 2.2b). Topology optimization aims at spreading a given amount of material in the
structure for a maximum stiffness. Here, holes can be automatically created during the
optimization process (Figure 2.2c). Finally, the optimization of the material can be addressed,
e.g. the local design of laminated composite structure with respect to fibers orientations, ply
thickness and stacking sequence (Figure 2.2d).
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