Composite Materials Research Progress

Optimization of Laminated Composite Structures… 67
4. Specific Problems in the Optimal Design of Composite
Structures
For designing laminated composite structures a very large number of data must be considered
(material properties, plies thickness and fibers orientation, stacking sequence) and complex
geometries must be modelled (aircraft wings, car bodies). Therefore the finite element method
is used for the computation of the structural mechanical responses. Usually mass, structural
stiffness, ply strength and strain, as well as buckling loads are the functions used in the
optimization problem. The design variables are classically the parameters defining the
laminate: fibers orientations, plies thickness, and indirectly the number of plies and the
stacking sequence. Some specific problems appear in the formulation of the optimization
problem for laminated structures. They are reported hereafter.
Large number of design variables. Even for a parameterization in terms of the lamination
parameters, the number of design variables can easily reach a large value when the plies
thickness and fibers orientations are allowed to change over the structure, leading to non
homogenenous plies (Figure 4.1) and curvilinear fibers formats (Hyer and Charette 1991,
Hyer and Lee 1991, Duvaut et al. 2000). In industrial applications (Krog et al. 2007),
thicknesses related to specific orientations (0°, ±45°, 90°) are used and several independent
regions are defined throughout the composite structure, what increases the number of design
variables.
Large number of design functions. Not only global structural responses related to the
stiffness are relevant in a composite structure optimization, but also the local strength of each
ply. Damage tolerance and local buckling restrictions are important as well. For an aircraft
wing, it is usual to include about 300000 constraints in the optimization problem (Krog et al.
2007).
Non homogeneous ply
Homogeneous ply
Figure 4.1. Homogeneous and non homogeneous ply in a laminate.
Problems related to the topology optimization of composite structures. In topology
optimization one is looking for the optimal distribution of a given amount of material in a
predefined design space that maximizes the structural stiffness (Figure 4.2).